Asked by Sky's chief political correspondent Jon Craig whether he would stand, Mr Streeting replied: "We need a proper contest with the best candidates on the field, and I'll be standing."
Mr Streeting said he did not want to force an immediate contest, as it "wasn't in the party's interest [or the] national interest" to have one before Andy Burnham has had the chance to return to parliament.
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The former health secretary said going ahead with an immediate battle would mean "the new leader, whether it was me or anyone else, would lack the legitimacy and so we would end up extending instability and uncertainty".
"If you think you're good enough to do the top job, if you think you've got the right ideas for the country, you should be prepared to put them forward, test them against other competitors, and win an election," he said.
The Ilford North MP was speaking at a conference of the Progress group of Labour supporters, who view themselves as being on the modernising wing of the party.
At the meeting, Mr Streeting described Britain's 2016 referendum decision to leave the European Union as "a catastrophic mistake" that had made the country its weakest since before the Industrial Revolution.
And he said the UK should seek to rejoin the bloc.
"We need a new special relationship with the EU, because Britain's future lies with Europe, and one day - one day - back in the European Union," he said.
Mr Streeting repeated his call for Sir Keir to "set out a proper leadership timetable", and to "give his ministers the freedom to nominate whoever they want to see as leader of our party and the prime minister of our country".
The PM has rejected calls to step down after his party suffered heavy defeats in local and devolved elections last week.
Meanwhile, Mr Burnham has been allowed to stand in the selection process for the upcoming Makerfield by-election - which could give him a route back to parliament and then possibly the keys to No 10.
The Greater Manchester mayor wants to be the party's candidate in Makerfield, although is yet to be officially selected, and said he is seeking to "save" Labour.
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Makerfield's current MP, former minister Josh Simons, is standing down specifically to try to give Mr Burnham the chance to return to the Commons.
Speaking to the BBC, Mr Burnham said the by-election is a "moment to reclaim the Labour Party, to save it from where it's been".
"You know we can't just carry on as we are. We're going to change the conversation in this campaign. We're going to get Labour closer to these communities again."
Mr Burnham also said Labour "needs to be better" and that politics has "not been working for people".
On Friday evening, the mayor was granted permission to run by Labour's ruling body, the National Executive Committee (NEC).
If Mr Burnham is successfully elected in Makerfield, he is widely expected to challenge Sir Keir for the party leadership.
While the constituency is typically a safe seat for Labour, the party expects a strong challenge from Reform UK this time around.
Mr Streeting quit as health secretary on Thursday and wrote a stinging resignation letter to the prime minister.
No formal leadership challenge has yet been triggered.
Huge amounts of jamming and spoofing have been detected around the Strait of Hormuz, as militaries seek to fight off drones and shadowy oil tankers try to evade detection.
Multiple countries in the Gulf are carrying out GPS disruption, electronic warfare expert Dr Thomas Withington from the RUSI thinktank told Sky News, pointing not just to Iran but to the US and other Gulf states.
Iran, he says, has mastered the technology.
Analysis from Windward, a maritime intelligence company, shared with Sky News shows there have now been more than a million GPS jamming incidents in the Middle East Gulf since the start of the war - accounting for 98% of all incidents across the world.
It's not hard to find evidence of it either. A look at a ship tracking map of the Strait of Hormuz shows odd things: tankers appearing to zoom across dozens of miles at wild angles, or huge clusters of vessels apparently stacked on top of each other.
All evidence that GPS-reliant systems are being fooled.
The evolution of GPS disruption
The ability to mess with GPS - the system we use to navigate day in, day out - has now become a routine part of modern war. And it's not confined to the battlefield.
In September 2025, a plane carrying EU chief Ursula von der Leyen suffered suspected GPS jamming.
The EU said the plane was able to land safely, adding: "We have received information from Bulgarian authorities that they suspect this blatant interference was carried out by Russia."
Two pilots previously spoke to Sky News about their experiences with jamming, and the impact it has on the aviation industry.
The use of GPS disruption at sea is not new either - it's a well-known occurrence in the Black Sea around Russian-held ports - but the sheer scale of it has rocketed since the start of the Iran war.
A look at a map of jamming or spoofing in and around the Strait of Hormuz shows large areas where GPS is hugely degraded, affecting everything from drones to passenger jets.
The result is that despite the Strait of Hormuz crisis being confined to a relatively small geographic area, figuring out what is going on can be tricky.
Which countries are jamming in the Gulf?
To increase its capabilities, Iran has bought jamming equipment from Russia and developed its own systems, says Dr Withington.
"The sheer saturation of jamming [in the region] is very much a reflection of what has been anticipated in the event of any confrontation between Iran and anyone else," he told Sky News.
GPS jamming was seen in the build-up to the US operation to remove Nicolas Maduro from Venezuela, and it would seem the Americans are also utilising GPS disruption in the Gulf, Dr Withington says.
Others in the Gulf "will absolutely be doing it", he added. "Probably more around airports, oil refineries, perhaps railway terminals, that kind of thing. The sort of critical national infrastructure that could be a target."
Elsewhere in the Middle East, Israel has long been accused of GPS jamming - to such an extent that Israeli and Lebanese civilians have reportedly matched on dating apps as the disruption messes with their device location.
RUSI security analyst Noah Sylvia previously told Sky News how Israel uses spoofing to impact the accuracy of cheaper munitions used by Hezbollah and Hamas that might navigate via GPS.
Using 'spoofing' to hide oil tankers?
One of the areas that Iran has used GPS disruption to increasing effect has been through its "deceptive shipping practices", senior maritime intelligence analyst Michelle Wiese Bockmann says.
Before the war, Iranian tankers would gather in international waters and then "spoof" their location to make it look like they are still there, she says.
But instead they will actually be sailing "dark" (with their AIS shipping trackers off) to Iran's Kharg Island where they can take on oil before returning to their original location.
There they may do a ship-to-ship transfer of cargo before a tanker sets off carrying its sanctioned cargo. It may be thousands of miles away before it reappears on public ship tracking, Ms Bockmann says.
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All this gives rise to questions over whether GPS can continue to be a reliable method of navigation.
"Absolutely," says Simon Cooper from QinetiQ, a defence company working in the UK on anti-GPS jamming technology.
"Global navigation and satellite constellations are hugely important to our everyday world and they'll continue to be in the future," he said.
"What's really important is to understand how they operate in different environments and to create the conditions whereby they can maintain their resiliency."
The WHO said 80 suspected deaths, eight laboratory-confirmed cases and 246 suspected Ebola cases had been reported as of Saturday in DRC's remote Ituri province across at least three health zones, including Bunia, Rwampara and Mongbwalu.
Africa Centres for Disease Control and Prevention (Africa CDC) said on Saturday at least 87 people had died in the eastern province, with 336 suspected and 13 confirmed cases recorded. Four people have died among the confirmed cases.
In Uganda's capital, Kampala, two apparently unrelated laboratory-confirmed cases, including one death, were reported on Friday and Saturday, from people travelling from the DRC, the WHO said.
The Ugandan health ministry said the cases were "imported" from the DRC and the body of the patient who died in Kampala was later taken back to the DRC.
A laboratory-confirmed case was also reported in the DRC capital, Kinshasa, from a person returning from Ituri, the United Nations health agency added.
The WHO said the outbreak does not meet the criteria of a pandemic emergency.
Africa CDC has raised concerns about the risk of further spread of the disease due to the proximity of affected areas to neighbouring Uganda and South Sudan.
The agency also warned of an "active community transmission" as health workers raced to intensify screening and contact tracing to contain the disease.
Difficulty tracking cases
Africa CDC director-general Dr Jean Kaseya said the first cases were reported in Mongwalu health zone, a high-traffic mining area, before migrating to the Rwampara and Bunia "as patients sought medical care, enabling spread across three health zones".
Of the 87 deaths, 57 are in the Mongwalu health zone, 27 in the Rwampara health zone and three in Bunia, Ituri's main city.
Mr Kaseya said a large number of active cases remain within Mongwalu in particular, "significantly complicating containment and contact tracing efforts".
Ongoing attacks by Islamic State-backed militants are also restricting surveillance and rapid response operations in Ituri, he added.
Congolese Health Minister Samuel-Roger Kamba said late Friday the suspected index case in the current outbreak is a nurse who died at a hospital in Bunia.
Mr Kamba said the case dates back to 24 April. He said the nurse presented with symptoms suggestive of Ebola, but he did not say whether samples from them were tested.
DRC has experienced 17 Ebola outbreaks since the disease was first identified in the country in 1976.
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One of the deadliest outbreaks, between 2018 and 2020 in eastern Congo, killed more than 2,000 people.
The country's eastern regions are also facing ongoing violence involving armed groups, including the M23 rebel movement and the Islamic State-linked Allied Democratic Force, complicating efforts to contain the disease.
Dr Gabriel Nsakala, a public health professor involved in previous Ebola responses in DRC, said the country had extensive experience dealing with outbreaks but warned rapid action would be essential.
"In terms of training, people already know what they can do," he said. "Now, the expertise and equipment need to be delivered quickly."
Five Italians, including a professor and her daughter, died in a scuba diving accident on Thursday.
Italy's foreign ministry said the group had been exploring caves in the Vaavu Atoll at a depth of around 50m (165ft).
The fifth victim was confirmed by the Maldivian government as being diving instructor Gianluca Benedetti, whose body was recovered on Thursday.
On Saturday, Maldives President Mohamed Muizzu confirmed a sixth death, Staff Sergeant Mohamed Mahudhee.
In a statement, he said: "The death of a diver of the Maldives National Defense Force while diving in search of missing tourists is a matter of deep sorrow for me and for every Maldivian citizen. This is heartbreaking news."
The search was suspended after the diver died of underwater decompression sickness after being transferred to a hospital in the capital, Maldives presidential spokesman Mohamed Hussain Shareef said.
Authorities are awaiting the arrival of three Finnish divers, experts in deep and cave diving, on Sunday, to rethink their search strategy, he added.
"The death goes to show the difficulty of the mission," Mr Shareef said.
Search operations on Saturday involved eight local divers working in shifts to find the missing Italians, the Italian foreign ministry said.
Italy's foreign minister Antonio Tajani said everything possible would be done to return the victims.
The University of Genoa named four of the victims as professor of ecology Monica Montefalcone, her daughter Giorgia Sommacal, who was a student, research fellow Muriel Oddenino, and marine biology graduate Federico Gualtieri.
In a statement posted on its website, the university said: "The sympathy of the entire university community goes out to the families, colleagues and students who shared their human and professional journey."
A second attempt at searching for the remaining bodies started on Saturday after rough weather repeatedly hampered the effort on Friday.
Mr Shareef said that Mr Benedetti's body had been found near the mouth of a cave, adding that it was believed that the remaining four had entered it.
Two Italians - a deep-sea rescue expert and a cave diving expert - were expected to join the recovery effort, Mr Shareef said.
Ms Montefalcone's husband, Carlo Sommacal, told Italian outlet La Repubblica that his wife was an "expert" and had done 5,000 dives.
"She knows what to do even in times of difficulty," he added.
Mr Sommacal said the same goes for Mr Benedetti, who he described as "meticulous", and said: "He checked everything: the tanks, the weather conditions. He's not a fool."
He said he hopes his wife and daughter's bodies are found for his and his son Matteo's sake, but also because "Monica usually had a GoPro when she went diving".
"I don't know if she had one the other day. If they find it, maybe from there we can understand what happened," he said.
Ms Montefalcone was an award-winning marine biologist, well known for her TV appearances and commitment to conservation projects, and was previously interviewed on Sky TG24.
"I have dedicated my entire life to discovering and studying the wonders that live beneath the surface of our seas," she told a local TV station, according to Sky TG24, after receiving the 2022 Atlantide Prize for her contribution to the understanding of marine ecosystems and her commitment to marine conservation.
The divers were reported missing at around 1.45pm by the crew of a diving vessel they were travelling on, when the group failed to resurface.
Conditions were described as unfavourable at the time, with a yellow weather alert in effect.
A large-scale search and rescue operation was launched by the Maldivian Coast Guard and the Maldives National Defense Force (MNDF). Boats, aircraft and dive teams were deployed to the area.
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"A body has been found among the five divers who dived in Vaavu Atoll," the MNDF said in a statement to Italian news agency ANSA.
"The body was found inside a cave. The other four divers are believed to be inside the same cave, which extends to a depth of approximately 60m."
Italy's foreign ministry added that the Italian embassy in Sri Lanka was working to contact the victims' families and provide consular assistance.
Four people are in a serious condition, the city mayor Massimo Mezzetti told broadcaster RaiNews24.
He said a woman was pinned against a shop window and required the amputation of both legs.
Police said they arrested the driver, a man in his thirties, and there was no further danger.
The driver is an Italian national born in Bergamo and a resident of the Modena area, the mayor added.
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"It seems (the driver) deliberately drove onto the sidewalk, hitting several people and crashing into a shop window. He then got out of his car and brandished a knife," said Mr Mezzetti.
He tried to flee but was stopped by some of the citizens involved in the crash and then by police, and was taken to headquarters for questioning.
One man who attempted to stop the driver suffered minor injuries, the mayor added.
Authorities are working to determine whether the driver was under the influence of substances or acted deliberately, the mayor said.
Witnesses reported the man was holding a knife, but he did not manage to stab anyone, the mayor said.
Victims were taken to hospitals in Modena and Bologna, with some of the most critical cases taken by helicopter.
"I express my solidarity with those who were injured and their families," Prime Minister Giorgia Meloni said in a post on X.
"What happened in Modena is extremely serious," Ms Meloni added.