A US-UK trade deal "will absolutely be possible", US President Donald Trump has said, after he told The Sun that Theresa May's Brexit plan could kill an agreement.
Speaking after talks at Chequers, the prime minister's country residence, Mr Trump said the US-UK relationship was "the highest level of special", while Mrs May said they had discussed plans for an "ambitious" trade agreement.
Mr Trump and his wife, Melania, later had tea with the Queen at Windsor.
Thousands of people have protested in London against Mr Trump's UK visit.
A large balloon, portraying the president as a baby, has been floated in Parliament Square as part of the demonstrations. Other protests are taking place across the UK on Friday and Saturday.
The Queen greeted Mr Trump and the first lady as their motorcade arrived at Windsor Castle. The band of the Coldstream Guards played the Star-Spangled Banner and she invited the president to inspect the guard of honour.
Their meeting lasted nearly an hour and was the final engagement in Mr Trump's two-day working visit to the UK.
The Trumps later took off from Windsor in a presidential helicopter on their way to Scotland for a weekend stay at his Turnberry golf resort.
Mr Trump and Mrs May's talks at Chequers took place after the Sun published its wide-ranging interview with the president in which he was critical of the PM's Brexit plan.
But standing alongside Mrs May after the meeting at her country residence, Mr Trump praised her as an "incredible woman" and a "very tough negotiator" who was "doing a fantastic job", and said there could be a "great" trade deal between the US and UK.
He said: "I read reports where that won't be possible, but I believe after speaking with the prime minister's people and representatives and trade experts it will absolutely be possible".
Mr Trump's first visit official visit to the UK as president took place in between the Nato summit in Brussels and a meeting on Monday in Helsinki with Russian leader Vladimir Putin.
At the news conference, Mr Trump said: "The relationship between our two nations is indispensable to the cause of liberty, justice, and peace."
He also told reporters:
- He had apologised to Mrs May for the Sun's story - but she told him not to worry as "it's only the press"
- He had not given Mrs May advice on how to deal with the EU but "did give her a suggestion... and I think she found it maybe too brutal"
- Brexit was an "incredible opportunity" and "whatever" the UK did after it left the EU was "OK with me"
Mr Trump described Brexit as a "very tough situation... between the borders and the entries into the countries and all of the things", saying: "The only thing I ask is that she work it out so that we can have very even trade."
Mrs May said the US was "keen" to do a deal with the UK, adding: "We will do a trade deal with them and with others around the rest of the world."
She maintained the government's Brexit agreement, which has come under fire from supporters of a "hard Brext" "delivers" on the referendum vote.
Earlier, Mr Trump said he and Mrs May had spoken for an hour-and-a-half at the black-tie dinner at Blenheim Palace, which he attended with his wife Melania.
"I think we probably never developed a better relationship than last night," he said.
Mr Trump arrived at the prime minister's Buckinghamshire residence by helicopter after visiting the Royal Military Academy at Sandhurst, Berkshire, on Friday morning.
Meanwhile, Mrs Trump played bowls with the PM's husband, Philip May, at the Royal Hospital Chelsea in London. She met Chelsea Pensioners and local children.
Downing Street said Mrs May had presented the US president with a gift of an illustrated ancestral chart of his Scottish heritage through his mother, and his wife with a bespoke perfume called the First Lady in a custom bottle.
In his Sun interview, Mr Trump also said former Foreign Secretary Boris Johnson - who disagrees with the PM on Brexit and resigned this week - would make a "great prime minister", adding: "I think he's got what it takes."
At the Chequers news conference, Mr Trump said he had been responding to the Sun's question about Mr Johnson as a possible prime minister, adding: "He has been very nice to me. He's been saying very good things about me as president."