Donald Trump has insisted the US-UK relationship is "the highest level of special", hours after he t
Donald Trump: US-UK relationship 'highest level of special'
Speaking alongside the PM, Mr Trump said Brexit was an "incredible opportunity" and "whatever" the UK did after it left the EU was "OK with me".
Mrs May said they had discussed plans for an "ambitious" trade agreement.
Thousands of people are protesting in central London against his visit.
A large balloon, portraying the president as a baby, has been floated in Parliament Square as part of the demonstrations. Other protests are due to take place across the UK on Friday and Saturday.
Mr Trump's first visit official visit to the UK as president is taking place in between the Nato summit and a meeting in Helsinki with Russian leader Vladimir Putin.
The president and first lady are travelling to Windsor to meet the Queen, before flying to Scotland to spend the weekend at Mr Trump's Turnberry golf resort.
Anti-Trump protesters are staging demonstrations in central London
The meeting between Mr Trump and Mrs May took place after the news broke that the Sun had published a wide -ranging interview with the president.
At a news conference following talks at the prime minister's country residence, Chequers, Mr Trump said: "The relationship between our two nations is indispensable to the cause of liberty, justice, and peace."
On a trade deal 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".
He said the US is looking forward to finalising a "great" bilateral trade agreement with UK.
He also said:
- He had apologised to Mrs May for the Sun's story - but she told him not to worry as "it's only the press... I thought that was very professional"
- "This incredible woman right here is doing a fantastic job, a great job"
- He said 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"
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 "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 on Thursday, which he attended with his wife Melania.
"I think we probably never developed a better relationship than last night," he said.