As he prepared to depart for London, the prime minister confirmed he was dispatching national security adviser Jonathan Powell to Geneva for talks with US officials, other European security advisers and Ukrainian representatives - as Europe and Ukraine scramble to reinsert themselves into a plan drawn up between Washington and Moscow.
The prime minister said on Saturday there was "more to do on the plan" in the coming days and the focus now was to try to make progress in Geneva.
Follow the latest: European leaders raise concerns over plan for Ukraine
After speaking on the phone to Donald Trump, Downing Street said the pair agreed their teams would work together on the US leader's proposal in the Swiss city on Sunday.
Starmer also reiterated Britain's "steadfast support for Ukraine" in a call with President Zelenskyy - as allies try to swing this deal more in Ukraine's favour, with the UK and other international leaders clear on their concerns to limit the size of the Ukrainian army and give up territory to Russia.
But in his remarks on camera, the prime minister was at pains to neither criticise the current deal nor President Trump.
One figure told me that the PM wants to act as a bridge between the Europeans and the US and has been playing a "game of whack-a-mole" over the past couple of days in an effort to keep others from publicly saying the deal is unacceptable for fear it would only serve to irritate President Trump and hurt Ukraine.
Earlier, the prime minister said he would talk to his US counterpart in the coming days.
"I'm absolutely clear in my mind that President Trump wants a just and lasting peace, not just from the actions he's taken towards that end, but also from the private discussions that I've had with him," Mr Starmer said.
"So I know what he's trying to achieve. We all want to achieve that."
But there will be a question about what the alternative options are if allies cannot improve this deal by President Trump's Thursday deadline.
The first option is to try to improve it and also slow down the process and buy more time, but if that fails, are allies looking at scenarios where they try to shore up Ukraine's war efforts without the US support?
The prime minister responded by talking about point five in the 28-point plan, in which Ukraine is offered security guarantees from the US.
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"That fortifies in me the belief that what we're all trying to achieve here is a just and lasting peace will only be just as lasting if there are security guarantees," Mr Starmer said.
"And if we bear in mind that matters for Ukraine are always to be determined by Ukraine."
The next 24 hours will be critical as the Europeans, Ukraine and other allies try to improve this deal.
Leaders and senior government officials from around the world have gathered in South Africa for the summit, which aims to make progress on solving some of the problems which are afflicting the world's poorest nations.
However, the conflict between Ukraine and Russia is also on the agenda following the release of a draft copy of a US-backed 28-point peace plan.
Follow the latest on the Ukraine peace plan
It closely resembles the list of demands repeatedly stated by the Kremlin since it launched its full-scale invasion of Ukraine nearly four years ago.
The plan, if adopted, would see Ukraine cede territory to Russia - and cut the size of its military.
Trump plan 'requires additional work'
Sir Keir told reporters in Johannesburg: "We are concerned about [caps on military], because it's fundamental that Ukraine has to be able to defend itself if there's a ceasefire."
He added the proposal, which will be discussed by US, Ukrainian and European national security advisers (NSAs) in Switzerland on Sunday, "requires additional work".
"It requires additional work, and that we are going to engage on that," said Sir Keir.
"And that's why there's been the agreement that in Geneva tomorrow [Sunday], you'll have senior US personnel, you'll have European NSAs, including the UK NSA, and obviously Ukrainians there to work further on the draft."
President Trump has said he wants a response to the peace plan from Ukraine by Thursday.
Asked about the deadline, Sir Keir said: "Obviously, I think it should be done as soon as possible, but it's got to be a just and lasting peace, and so we've got to get it right.
"I think we'll be in a better position to know once the meeting in Geneva has taken place tomorrow, because that's the opportunity for the US, Ukraine and European NSAs to go through quite a bit of detail."
Mr Trump's 28-point peace plan was "by far" not the "final offer", the US president told reporters outside the White House.
"We'd like to get the peace, it should've happened a long time ago. The Ukraine war with Russia should've never happened. If I was president it would have never happened," Mr Trump said.
"We're trying to get it ended. One way or another, we have to get it ended."
Sir Keir spoke to Ukraine's President Volodymyr Zelenskyy on Saturday, who said in a post on Telegram after the call: "We had a long conversation, discussed many nuances of diplomatic work in planning the peace process. We will continue to coordinate, and I am grateful to the entire British society for their support."
A Downing Street spokesperson said that the prime minister updated Mr Zelenskyy on the progress of talks of the self-styled coalition of the willing at the G20 meeting in South Africa.
Sir Keir also spoke to Mr Trump, relaying such discussions to the US leader, according to the spokesperson, who said the two leaders agreed their teams would work together on the 28-point peace plan tomorrow in Geneva.
Starmer and Trump also agreed to speak again tomorrow.
Sir Keir also told reporters about the G20 bloc's "critical" importance on its first day.
What is the role of the G20?
The role of the G20 is critical at this moment," said Sir Keir, who has defended his decision to fly to the G20 days before a difficult budget.
"Growth must be a mission for us all to embrace as the means to improve lives, fund public services and to keep our people secure.
"The G20 has worked together before to fix fundamental problems in the global economy. We need to find ways to play a constructive role again today in the face of the world challenges.
"I'd like to see us come together around a five-point plan for growth that leaves no one behind."
The US, however, is boycotting the talks.
The Trump administration made its opposition to South Africa's G20 agenda clear earlier this year when the country started holding meetings ahead of the summit.
Marco Rubio, the US secretary of state, skipped a foreign ministers meeting in February, and said that he would not waste American taxpayers money on an agenda which was focused on diversity, equity and inclusion and climate change.
South Africa gets to set the agenda as the country holding the rotating G20 presidency.
G20 leaders broke with tradition and adopted a declaration at the start of their summit - despite opposition from the US.
Vincent Magwenya, spokesman for South African president Cyril Ramaphosa, said a leaders' declaration was adopted unanimously in Johannesburg.
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Mr Magwenya said: "Normally the adoption of the declaration happens right at the end. But... there was a sense that we should actually move to have the summit declaration adopted first as the first order of the day."
There were no details of what was in the declaration, but South Africa has promoted it as a victory for the summit.
The G20 bloc was formed in 1999 as a bridge between rich and poor nations to confront global financial crises.
While it often operates in the shadow of the powerful Group of Seven nations, G20 members represent around 85% of the world's economy, 75% of international trade and more than half the global population.
The deal would boost finance for poor nations coping with global warming, but it fails to namecheck the fossil fuels driving it.
As the summit wrapped up in Brazil, applause masked disappointment in the many weak parts of the agreement. But what many were celebrating was that they'd agreed on anything at all.
With countries around the world fighting, cost of living crises and the United States missing from the talks altogether, many feared the process could unravel.
And two other similar forums this year - on green shipping and plastics pollution - fell apart entirely.
"It's a weak outcome," said former Philippine negotiator Jasper Inventor, now at Greenpeace International.
In the text of the draft deal, instead of a transition plan away from fossil fuels, the agreement "acknowledges that the global transition toward low greenhouse gas emissions and climate-resilient development is irreversible and the trend of the future," and says "the (2015) Paris Agreement is working and resolves to go further and faster."
Despite no transition plan being included in the deal, the summit's president Andre Correa do Lago said voluntary plans on fossil fuels and forests would be mapped out instead - with applause for Colombia, who will host a summit on the latter next year.
The annual United Nations conference brings together world leaders, scientists, campaigners, and negotiators from across the globe, who agree on collective next steps for tackling climate change.
The two-week conference in the Amazon city of Belem was due to end at 6pm local time (9pm UK time) on Friday, but it dragged into overtime, as is common for COP talks.
The standoff was between the EU, which pressed for language on transitioning away from fossil fuels, and the Arab Group of nations, including major oil exporter Saudi Arabia, which opposed it.
The impasse was resolved following all-night talks led by Brazil, negotiators said.
The European Union's climate commissioner Wopke Hoekstra said on Saturday that the proposed accord was acceptable, even though the bloc would have liked more.
"We should support it because at least it is going in the right direction," he said.
Brazil's President Luiz Inacio Lula da Silva and about 80 countries, including the UK and coal-rich Colombia, had been pushing for a plan on how to "transition away from fossil fuels".
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This is a pledge all countries agreed to two years ago at COP28 - then did very little about since.
But scores of countries - including major oil and gas producers like Saudi Arabia and Russia - see this push as too prescriptive or a threat to their economies.
UK Energy Secretary Ed Miliband told Sky News on Friday that while the UN climate talks are a "nightmare", they are the "best process we've got".
The annual COP talks are "so hard" because they see more than 190 countries negotiating over the future of their economies, oceans and forests, he said.
But he pointed to achievements from the three decades of talks, including lowering expected global warming by a substantial margin, and the fact that around 80% of global GDP is now covered by a net-zero climate target.
Mr Miliband said: "So it's painful, it's painstaking, it makes you tear your hair out, but it does represent progress.
"This is a global problem; we've got to have global cooperation to tackle it."
Local health authorities in Gaza said there had been four separate airstrikes.
One hit a car in the densely populated Rimal neighbourhood of Gaza City, killing 11 people and wounding several others, they said.
At least 13 people died in strikes on houses near Al-Awda Hospital in central Gaza, Deir al Balah and Nuseirat camp, according to health officials in Gaza.
They said at least 54 people, including children, have been injured in the four Israeli airstrikes.
The Israeli military said there had been a "blatant violation of the ceasefire agreement" after what it called an "armed terrorist" crossed into Israeli-held territory and shot at troops in southern Gaza. It said no soldiers were hurt.
In a statement, it said the gunman had exploited "the humanitarian road in the area through which humanitarian aid enters southern Gaza".
A Hamas official rejected the Israeli military's allegations as baseless, calling them an "excuse to kill", adding the Palestinian group was committed to the ceasefire agreement.
In a separate statement, Israel's military said its soldiers killed what it called five "terrorists" in two other incidents.
It said three were shot dead in the Rafah area, while two others were killed when they crossed into Israeli-held areas in northern Gaza and advanced toward soldiers.
The Israeli airstrikes are a further test of a fragile ceasefire with Hamas, which has held since 10 October following the two-year Gaza war.
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Israel pulled back its troops, and the flow of aid into the territory has increased. But violence has not completely halted.
Palestinian health authorities say Israeli forces have killed 316 people in strikes on Gaza since the truce.
Meanwhile, Israel says three of its soldiers have been killed since the ceasefire began and it has attacked scores of militants.
Dutch minister of defence Ruben Brekelmans said defence counter-drone measures were "ready to intervene".
The country's police and military are also on site, the minister added in a post on X, and an investigation is ongoing.
The airport in the south of the Netherlands is used for both military and civilian purposes. All types of air traffic had been halted, Mr Brekelmans said.
The Dutch military on Friday evening had used weapons against drones sighted above the air force base in Volkel, some
40 kilometres (25 miles) northeast of Eindhoven, the defence ministry had said earlier on Saturday.
Various airports in Europe were closed in September over drone sightings, including in Denmark and Copenhagen.
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