"We agreed today, that as the UK leaves the European Union, we will pursue an ambitious US-UK Free Trade Agreement", she said, adding: "The Chequers agreement reached last week provides the platform for Donald and me to agree an ambitious deal that works for both countries right across our economies".
"I actually told Theresa May how to do [Brexit], but she didn't listen to me", Trump said in the Sun interview, and then mused that May's Conservative Party rival, Boris Johnson, "would be a great prime minister".
Taoiseach Leo Varadkar has described the British White Paper on Brexit as an evolution of the UK's position, but he did not think it provided a solution to Brexit.
"We may be a small country, but we're a great one too", he continues.
Asked directly whether he thinks Johnson might someday replace May, he declined to comment, saying he wasn't interested in "pitting one against the other". "I think he has done a very bad job on terrorism". "It's called fake news", Trump said.
On Brexit, he said: "I don't know what you're going to do, but whatever you do, it's OK with me ... just as long as we can trade together".
He said it is something that can be inputted into the negotiations on future relationships.
Theresa May and Donald Trump enter Blenheim Palace for a dinner hosted by the British prime minister on the first day of the United States president's visit to Britain.
Trump's visit to Britain followed two days of a North Atlantic Treaty Organisation summit in Belgium, where the USA president shook up the conference with rhetoric about other members failing to meet fiscal defense requirements, the possibility that he could end the United States' 70-year membership in the alliance and Germany being "captive" to Russian energy.
Allowing the immigration to take place in Europe is a shame.
"It will certainly be something that we bring up and talk about", Mr Trump said.
Mr Trump and his wife Melania arrived at Stansted airport, where he was met by the UK's global trade secretary Liam Fox. "I think he has done a bad job on crime, if you look, all of the terrible things going on there, with all of the crime that is being brought in". Barriers where they won't take our farm products, they won't take many of our things, including our cars.
They reportedly dined on Scottish salmon followed by beef, then strawberries and clotted cream ice cream - traditional British fare created to impress.
The streets of London were packed with protesters Friday as up to 100,000 Brits were expected to publicly express their unhappiness with Donald Trump.
The petition against Trump claimed an official state visit would be embarrassing for the Queen.
Her trip to Europe marked the former model's return to the global stage after she was hospitalized for a kidney condition in May and dropped out of public sight for almost a month.
He first retold the false story in an interview with The Sun, a British newspaper.
The Sun is no stranger to publishing controversial material.
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