Speaking to reporters outside the White House, the US president added: "We actually know the people who made the threat."
The Pentagon confirmed on Sunday the removal of bombers, including B-1s, B-2s and B-52s, from the base in Gloucestershire.
The air base was the target of a suspected terror attack on 27 September. Five UK nationals in their mid-20s were arrested on suspicion of explosives offences and terrorism close to the military site.
They have since been bailed, as has a UK-Iranian national who was arrested on suspicion of preparation of terrorist acts on 1 October.
Asked if there was a "specific threat" that led to the removal of the US bombers, Mr Trump replied: "Yeah I think we can say that.
"They didn't fly out by accident.
"There were some threats. And rather than tempting the enemy, we'll capture the enemy and beat the enemy. But why should we leave them there? So we moved them around a little bit. Not very far."
It comes after US secretary of state Marco Rubio said the removal of the US bombers was not directly connected to the arrests of five men near the base.
"The Department of War is constantly reallocating resources where they need to be. There are regular rotations that happen as well," said Mr Rubio.
"We've documented what happened last week. I wouldn't directly tie that to the move that was made."
US vice president JD Vance said the decision to remove the bombers was taken "out of an abundance of caution" to "protect our guys".
He added: "We do feel with some confidence that the Iranians are, you know, they're trying to do what the Iranian state has done for 49 years, which is engaged in acts of terrorism against the United States (and others), so we are being extremely cautious, and that's all I'd say about that."
Asked on Monday whether RAF Fairford - a long-time home to US forces - remains safe, a spokesperson for UK Prime Minister Andy Burnham replied: "Yes."
The spokesperson said they "wouldn't comment on other countries' military decisions", and also declined to comment on whether the PM had spoken to Mr Trump about the decision.
They said there had been "no change to position" regarding the base and the government is "investing £470m into securing defence bases around the UK".
Three of the US planes landed in South Dakota on Sunday, anonymous US officials reportedly told The New York Times.
One said that more specific threat details had emerged in the 24 hours prior to the bombers being withdrawn.
Some aircraft and crew left while refuelling flights were still being arranged because of the urgency of the situation, according to the outlet.
A Pentagon official said on Sunday all US bombers at RAF Fairford had now been "redeployed to their home stations in the United States".
They said America's bomber force remained ready for "precision global strike capabilities", including through missions that begin and end in the continental US.
The prime minister said on Wednesday there was a "strong indication that Iran played a part" in the earlier incident. Iran has denied any involvement.
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Two Pentagon sources told Sky's US partner network NBC News the rushed withdrawal of at least 12 bombers included several that had just arrived as part of a rotation.
RAF Fairford is an important base for US military operations. It acts as the headquarters for the US 501st Combat Support Wing and the 420th Air Base Squadron, according to the unit's website.
It serves as "the preferred bomber forward operating location in Europe for US Air Force Global Strike Command".
In March, a number of US B-1 Lancer bombers arrived at the military base as part of US operations after launching the Iran war.
The best-selling author and politician died "suddenly and peacefully" at home, his publisher HarperCollins said.
Lord Archer was a Conservative MP for five years before serving as the party's deputy chairman. He enjoyed a successful career as a novelist - selling more than 300 million copies worldwide - and was made a life peer in 1992.
He had been a senior party official under Prime Minister Margaret Thatcher in the mid-1980s, however, his political career was paused in 2001 after being imprisoned for perjury and perverting the course of justice.
A jury found he had lied in a libel action he had brought against The Star newspaper in 1988, in which he was awarded £500,000 in damages. He was released from prison in 2003, returning to the House of Lords until his retirement in 2024.
Lord Archer's final novel, Adam and Eve, is due to be published later this month.
Conservative leader Kemi Badenoch said Lord Archer's death had come as "a huge shock", and that she was "incredibly saddened to hear this news".
Ms Badenoch added: "He had sent me a lovely message just this [Monday] morning and was always a great source of encouragement to me personally. I can't believe he's gone."
HarperCollins said Lord Archer had attended an event with fans in London on Sunday.
Broadcaster Gyles Brandeth, who was also at the event, wrote in a social media post: "Just yesterday I did a show with Jeffrey Archer to celebrate his new novel - he said it was to be his last.
"He was in the most wonderful, ebullient form and had such a great reception from a packed house. He was funny, engaging and self-deprecating - a great storyteller to the last."
Former Tory minister Nadhim Zahawi also paid tribute to Lord Archer, describing him as "an extraordinary human being".
Mr Zahawi added: "His gift for storytelling was matched by his wit, warmth and boundless energy. Life was never dull in Jeffrey's company."
Kate Elton, Lord Archer's editor and HarperCollins UK chief executive, said that working with him had been "one of the great privileges of my publishing life".
Ms Elton added: "He was the master storyteller and an editor's dream - phenomenally hard-working, utterly committed to completing draft after draft to get every word as perfect as possible, and a true champion of the 'team' nature of great publishing."
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The forecaster is among many predicting this year's El Nino will be "unprecedented" and will probably increase the chances of wetter, stormier conditions in the UK.
However, in a blog post, it took aim at recent headlines claiming freezing conditions and a "551-mile wall of rain and snow" are about to hit.
Britain's weather is normally less directly affected by El Nino, and the Met Office said recent reporting had been "dramatic".
El Nino is a phenomenon that happens every few years in which there's a warming in sea temperatures, typically in the equatorial Pacific.
It pushes up air temperatures and can lead to more extreme weather in places such as India, East Asia, South America and parts of Africa.
El Nino is expected to peak towards the end of the year - and a "dire warning" of an imminent "polar vortex of snow and storms" are unfounded, according to the Met Office.
It said El Nino "does not determine individual weather events" and the forecast didn't support the claim the UK is about to be "smashed" by widespread snow.
Another headline that predicted snow this week in "12 areas after polar vortex forecast" is also said to be well wide of the mark.
The Met Office said there was no indication of this, and any changes to the polar vortex caused by El Nino would occur at the end of winter.
So no digging out the car or making snow angels in the coming days - but widespread rain in England and Wales is expected on Wednesday.
Get the Sky News forecast for your area
Temperatures are also forecast to be average - or slightly below average - mid week. However, the Met Office said predictions of a "plunge" ushering in an "autumn chill" were also an exaggeration.
The cooler feel will quickly subside and Thursday and Friday will be near normal again, while Saturday is set to be "cool in places" with blustery winds, scattered showers and sunny spells.
"This is a recognisably autumnal pattern rather than an exceptional cold spell," said the Met Office.
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The forecaster also took issue with an overenthusiastic headline stating: "Weather maps turn green and red as UK 'disappears' under 551-mile wall of rain and snow".
Bands of rain are indeed in the short-term forecast, but the Met Office said an "unbroken wall of rain and snow" is not on the cards. The South in particular could get relatively little rain over the weekend.
"The overall message is therefore one of changeable autumn weather. Spells of rain, brisk winds, showers and some chilly intervals, but also drier periods," it added.
"Dramatic nationwide snow and prolonged freezing conditions are not the central themes of the current forecast."
While El Nino normally has a limited effect on UK weather this autumn and winter, the government has admitted the effects are "uncertain" due to the expected magnitude of this year's event.
According to flight tracking data, the service to Chicago took off from Heathrow Airport at around 12.15pm on Monday.
It declared a mid-air emergency and made a steep descent while flying over Ireland around half an hour later.
Flight tracking data shows the plane had reached its cruising altitude of 36,000 feet before dropping sharply to an altitude of 9,000 feet.
The plane then turned back and spent around four hours zigzagging over the Bristol Channel, before landing back at Heathrow at just after 5pm.
In a statement, British Airways said: "The aircraft landed safely after our highly-trained pilots returned to Heathrow following a technical issue.
"Customers disembarked the aircraft normally and our teams are working to get their travel plans back on track as quickly as possible."
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It is likely passengers will be provided with hotel rooms by the airline until another flight is made available, as stipulated by the UK Civil Aviation Authority.
The female researcher at the Irkutsk Anti-Plague Research Institute of Siberia and the Far East had died last week of "pneumonia of unknown etiology" or origin, according to the country's consumer welfare service.
It said the "sanitary-epidemiological situation" in the Irkutsk region and the cities of Irkutsk and Shelekhov was "stable".
Russian authorities said they found no evidence the researcher's illness was caused by any of the pathogens she worked with.
Almost 200 people who had been in contact with the researcher were now being observed, said reports citing a regional leader.
Maksim Modin, mayor of the Shelekhov municipal district near the border with Mongolia, said the inpatient facility where the researcher was treated had been closed for quarantine.
Russian authorities have not confirmed the 28-year-old researcher's exact cause of death.
The World Health Organisation (WHO) has said the pneumonic form of plague is especially contagious and "can trigger severe epidemics through person-to-person transmission via respiratory particles".
Asked to comment on the case, Kremlin spokesman Dmitry Peskov said the public and media should follow official statements rather than "rumours or speculation".
What are the symptoms?
According to the WHO, it is the most virulent form of plague and the incubation period can be as short as 24 hours.
Symptoms appear quickly - sometimes less than 24 hours after infection. They include severe respiratory symptoms such as shortness of breath and coughing, often with blood-tainted mucous.
How is it treated?
The WHO said pneumonic plague can be fatal within 18 to 24 hours of disease onset if left untreated.
But common antibiotics for enterobacteria can effectively cure the disease if they are given early.
How is it transmitted?
The WHO said: "Any person with pneumonic plague may transmit the disease via respiratory particles to other humans. Untreated pneumonic plague, if not diagnosed and treated early, can be fatal.
"However, recovery rates are high if detected and treated in time - within 24 hours of onset of symptoms."
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How easy is it spread from person to person?
Dr Ashish Jha, who was the White House COVID-19 response coordinator from 2022 to 2023, said "it's actually very hard" for pneumonic plague to spread from person to person.
Dr Jha said "much more" information and transparency was needed from Moscow.
If this is an isolated case of pneumonic plague and no one else dies then "it will probably end there", he told NBC News.
"If there were weapons programmes, biological weapons programmes in these labs, that would be much more concerning to me," he said. "We need to understand that now."
Ian Jones, professor of virology at the University of Reading, said: "This case here seems like a rare lab accident and is unlikely to go much further.
"Although it is true that pneumonic plague is directly transmissible, the contacts of the primary case are known and can be treated if they show any sign of infection.
"Plague carries a huge history and is still present in many parts of the world including Russia, but the living conditions associated with how it previously spread are no longer generally true, antibiotics are available and its potential is therefore limited."
From 2019 to 2025, 10 countries reported more than 3,800 suspected human plague cases to the WHO, the agency said last week.
Six of the countries had confirmed cases, most of them in the Democratic Republic of the Congo and Madagascar, with 423 deaths.