Speaking to Sky News' Wilfred Frost, Scott Bessent said: "My belief is that as soon as it is militarily possible, the US Navy, perhaps with an international coalition, will be escorting vessels through."
He added: "There are, in fact, tankers coming through now, Iranian tankers, I believe some Chinese flag tankers have come through. So we know that they have not mined the straits."
Supreme leader Mojtaba Khamenei plans to use the effective closure of the strategic waterway as leverage against the US and Israel.
As the war nears the two-week mark, Mr Khamenei, in a fiery opening address, promised retaliation for the US-Israeli strikes, saying he "will not refrain from avenging" the blood of their "martyrs" - as a new wave of Israeli strikes hit Beirut.
Iran's relentless attacks on shipping traffic and energy infrastructure in the Persian Gulf had earlier pushed oil back above $100 a barrel, with stocks dropping worldwide on Thursday.
The hike in oil prices came despite the shock announcement the previous day that developed countries would release 400 million barrels of oil from their strategic reserves - nearly half from the US.
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During the wide-ranging interview, Mr Bessent was called to the Situation Room, an intelligence facility in the West Wing of the White House, and when asked if the escort had been discussed, he did not deny it, saying: "Your words, not mine."
Speaking after the interview, Mr Frost said that while the market isn't expecting the safe passage of ships in any meaningful way in the days ahead, Mr Bessent's implication in the interview might suggest otherwise.
Earlier on Thursday, the US energy secretary, speaking to CNBC, ruled out the possibility that the US will imminently take action to escort oil traffic through the strait.
"It'll happen relatively soon but it can't happen now," Chris Wright said.
"We're simply not ready."
In the interview, Mr Bessent also mentioned that the war has so far cost the US around $11bn.
Mr Frost asked the treasury secretary if there was a price that could cause him to confront US President Donald Trump and say the war is no longer affordable.
He replied: "Absolutely not."
The economic turmoil comes in the wake of a row between Washington and London.
Mr Trump hit out at the UK again last week, saying the US does not need anyone to "join wars after we've already won" following its initial refusal to allow the US to launch its initial attacks on Iran from British bases.
Sir Keir Starmer later granted the US use of British facilities for "defensive" action against Iranian missile sites.
Questioned on the special relationship and whether Sir Keir had put lives at risk with his response to the Iran war, Mr Bessent, who has previously lived in London, said: "We delayed being able to fully implement the military plan, and I think that the main concern was the use of base Diego Garcia, and the US B-2s had to do a 37-hour round trip rather than, I think it's about a three, three-and-a-half-hour round trip and constantly refuelling.
"So I think any delay causes an increase in risk."
He added: "President Trump is the commander-in-chief of US forces. Being in the Situation Room with him, he so solemnly takes that leadership role in terms of his commitment to maintaining the lives of our servicemen.
"Anything that upsets that, upsets him, and I think that's what got the very strong reaction."
But Mr Bessent also recognised that the two nations have a "great historical relationship".
When asked how unhappy Mr Trump is with the prime minister right now, he said: "Belatedly, the prime minister offered to put resources in the region. We have a long-term relationship."
He noted that while there will be "some bumps in the road", he thinks the relationship will "eventually get back on track".
On whether Peter Mandelson and Andrew Mountbatten-Windsor should testify to Congress, the US treasury secretary said: "That's a matter for Congress."
He added: "If Congress requests for you to come, you should come."
The full interview of "The Master Investor Podcast with Wilfred Frost" is available to watch on YouTube or to listen wherever you get your podcasts.
Amanda Wixon, 56, forced the woman - now in her 40s - to shave her hair, regularly beat her if she didn't complete jobs around the home, and made her live off "scraps" of food.
It's also understood that while being held, Wixon, a mother of 10, stole more than £100,000 in benefits from the victim.
Wixon will serve two-thirds of her sentence.
Police officers who arrived at the house in Tewskesbury, Gloucestershire, following a tip-off from one of Wixon's sons in March 2021, described the victim's bedroom as looking like a "prison cell".
They found a basic bed with filthy sheets, bare plaster walls with mould growing on them and no light bulb.
The woman, who we can only identify as "K", has learning difficulties and knew Wixon when she was a child, through family connections.
In 1996, she was taken into Wixon's home at the age of 16.
Police say that Wixon kept her in squalid conditions for more than two decades, forced her to look after her children, locking her in the house and depriving her of food, health and dental care.
The jury heard she was beaten with a broom handle, knocking out her teeth, had washing-up liquid squirted down her throat and bleach splashed on her face.
Wixon did not allow "K" to wash herself, something she did in secret at night.
The court heard how Wixon had strangled the victim and pushed her head down the toilet.
Wixon had benefits for the victim paid into her bank account from the late 1990s, receiving more than £100,000 over the years.
After being removed from the address, doctors described "K" as "malnourished" - noting scarring around her mouth, thought to be due to contact with cleaning fluids.
Calluses were found on her ankles, consistent with the victim's account of spending hours on her knees sweeping the floor.
During sentencing, Judge Ian Lawrie KC said Wixon was in "permanent denial" about her offending.
"The gravity of your offending is so serious that I am imposing a significant period of custody," he said.
He added: "This offending was not isolated and was persistent over many years."
'Nothing can give back the years lost'
The victim now lives with a foster family, attends college and has been on holidays abroad.
In a statement read to the court, the victim said: "For 25 years, I lived in fear, control and abuse. I was treated as though my life, my freedom and my voice did not matter.
"Although my abuser has now been found guilty, the trauma and the nightmares are something I still carry with me every day."
She added: "Nothing can give me back the 25 years I lost."
K's new foster mother described how she "had to take her to the doctors and get lots of appointments and try and feed her and show her love... She wasn't used to things like that".
She described how when K first arrived to live with her, "she didn't want me to hug her", but that after weeks of support and hard work, she "turned around and started being loving".
Wixon was convicted in January at Gloucester Crown Court of modern-day slavery offences, including two counts of requiring a person to perform forced or compulsory labour, one count of false imprisonment and three counts of assault occasioning actual bodily harm.
She was found not guilty of a further count of assault.
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Outside court, Gloucestershire Police detective chief inspector Dave Shore-Nye said: "There is no prison sentence that could reflect the pain and suffering (Wixon) has inflicted on the victim, or bring back the decades she stole from her."
Detective Superintendent Ian Fletcher, from Gloucestershire Constabulary, said this was one of the "worst cases" he had ever seen.
"The pure longevity of the harm that's been caused, nearly 25 years of suffering and pain. This is one of the most horrific crimes I've seen investigated by Gloucestershire."
Huge crowds formed on Thursday to catch a glimpse of the pair - who even pitched in by serving customers.
Kate made husband William a coffee - only for him to turn it away when he realised it wasn't decaf.
Elsewhere she told a brewer that she had to stay clear of alcohol because of her cancer diagnosis.
The Princess of Wales showed off her barista skills during a stop at Change Please, a social enterprise training homeless people in coffee retail.
She handed the finished drink to her husband, saying "I've made a coffee for you, William", but when he asked "is it decaf?" and she replied "no", he suggested it should be sold.
Kate carried the coffee with her when they carried on with their tour of the popular attraction that has been a focus for food lovers for decades.
Staff member Lorent Maliqi said afterwards: "She did really well.
"I was surprised, she got the texture of the milk right on point - it was a great effort."
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William and Kate were hands-on throughout their visit, which began at the Trethowan Brothers stall where award-winning cheese made from their farm in north Somerset has been sold since the early days of Borough Market almost 30 years ago.
They went on to sample some handmade Pitchfork Cheddar, made with unpasteurised milk, and the Gorwydd Caerphilly cheese, and told Todd Trethowan: "That's lunch taken care of."
They then moved behind the counter, cutting a wedge of Caerphilly cheese under Mr Trethowan's guidance, before Kate used the wire to slice some of the cheddar, which was bagged and handed to the couple's aide for later.
Dozens of onlookers packed out the busy central London market to get pictures of the pair.
The pair then spoke to Kim Innes, who runs Humble Crumble, as she dished out servings of crumble to customers.
"They were really keen to do it and really good at it, and they put on aprons and everything," Ms Innes said.
"They were both encouraging each other and were complimentary about each other's work."
Earlier in the day, the pair were declared winners in a pint pulling contest against the founder of a brewery, as they visited London's Bermondsey Beer Mile.
They were invited to try beers and ciders at the Fabal Beerhall, and went behind the bar at the Southwark Brewing Company.
Kate asked brewer Hannah Rhodes if they had any non-alcoholic beers, saying she had to stay clear of alcohol since her cancer diagnosis.
"She said something along the lines of 'since my diagnosis it has been best to avoid alcohol'," Ms Rhodes told the Press Association.
They were not hurt.
John Healey said attacks by Iranian forces against targets across the Middle East "have the hallmarks" of how Russian troops operate in their war against Ukraine.
This included a change in how Iran uses its drones.
Tehran sold thousands of "Shahed" one-way attack drones to Russia in the early months of President Putin's full-scale invasion of Ukraine.
The Russians, with Iranian help, then developed their own version of the unmanned aerial vehicle and now the lessons they have learnt from fighting in Ukraine appear to be helping the Iranians in their response to waves of US and Israeli strikes against Iran.
"No one will be surprised to believe that Putin's hidden hand is behind some of the Iranian tactics, potentially some of their capabilities as well," Mr Healey said, speaking to reporters during a trip to the UK's Permanent Joint Headquarters (PJHQ) at Northwood, the main base overseeing military operations overseas.
The defence secretary said this likely Russia link was "not least because the one world leader benefitting from the sky high oil prices at the moment is Putin".
He was referring to a spike in the price of oil after Iran used its chokehold over the Strait of Hormuz off its coastline to block one of the world's most vital shipping lanes.
The defence secretary said the Russian president "is clearly likely to welcome this war more than anyone else."
Lieutenant General Nick Perry, the chief of joint operations who oversees all UK military operations around the world, said there was "definitively" a link between Russia and Iran, which have a long-standing military relationship.
"We have definitely seen the Iranian tactics of the use of their drones learnt from Russians - flying them much lower so they are more effective," Lieutenant General Perry said, speaking to Mr Healey as they looked at a map of the Gulf in a room at the military headquarters.
"There is no doubt [the Iranian] tactics have changed," Lieutenant General Perry said.
He said drones were causing the most damage by the Iranian side across the region.
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This included an Iranian-linked drone - potentially fired from Lebanon or Iraq - that struck a Royal Air Force base in Cyprus on the second day of the war, landing near a hanger.
Mr Healey said the components of that device are being investigated to find out if they included Russian parts.
"We will update you on the findings from that," he said.
A second military commander said that British forces had shot down two drones fired towards a military base in Erbil, northern Iraq, overnight.
"A number did impact the camp," the officer told Mr Healey.
He said there had not been any British casualties.
However, the defence secretary said there had been reports of a number of US casualties, though none had been seriously injured.
Former police officer Jeff Blair, 55, died after being assaulted in Shildon, County Durham, at around 1pm on Tuesday.
He sustained serious injuries and was pronounced dead after being taken to James Cook University Hospital in Middlesbrough.
Robert Davies, 49, has been charged with murder, possession of an offensive weapon, and affray.
He has been remanded in custody ahead of an appearance at Peterlee Magistrates' Court on Friday.
Mr Blair worked as a police officer for Durham Constabulary for 22 years before retiring in 2017 prior to becoming a bailiff.
Detective Chief Inspector Sharon Alderson, who is leading the investigation, said: "This has been a deeply upsetting incident which has caused a great deal of shock to the local community.
"Our thoughts are with Jeff's family and all those who knew and loved him at this difficult time.
"We will continue to have a police presence at the scene, and I'd like to thank the public and nearby residents for their patience, understanding, and co-operation while we work to establish exactly what has happened.
"We are keen to hear from anyone who witnessed the incident, or who has any information that could help the investigation and has not yet spoken to us."
Police are asking anyone with information to call Durham Constabulary on 101, quoting incident reference 209 of 10 March.