Referring to May's Brexit proposals, Trump told the Sun, Britain's top-selling newspaper: "If they do a deal like that, we would be dealing with the European Union instead of dealing with the United Kingdom, so it will probably kill the deal".
"I think he has done a bad job on crime, if you look, all of the frightful things going on there, with all of the crime that is being brought in", he said.
"What we are doing is delivering on the vote of the British people. that's what our proposal does", she told reporters at a North Atlantic Treaty Organisation summit in Brussels.
She said: "Many of the intentions are reassuring".
Our Brexit Insider Facebook group is the best place for up-to-date news and analysis about Britain's departure from the European Union, direct from Business Insider's political reporters. "I would actually say that she probably went the opposite way".
"It's an opportunity to reach a free trade agreement that creates jobs and growth here in the UK and right across the United States".
I am just saying I think he would be a great Prime Minister. It was one of over a hundred protests police expected during Trump's four-day trip.
As Britain prepares to leave the European Union on March 29, 2019, supporters of Brexit have made much of the so-called special relationship with the United States and the benefits of forging closer trade ties with the world's biggest economy.
Former Conservative party leader Iain Duncan Smith said he had "deep misgivings" about the white paper; veteran Brexit hardliner Bill Cash declared himself "deeply anxious;" and Andrew Bridgen, who has already sent a letter expressing no confidence in May to party authorities, said he "and many colleagues" had "grave concerns" about the path the government is now on, Politico reported.
Britain is now part of the EU's single market - which allows for the frictionless flow of goods and services among the 28 member states - and its tariff-free customs union for goods.
Labor officials are not talking about their tactics for the coming battles but, according to Politico, have spoken privately about a "coalition of chaos" where their MPs would vote with Brexit hardliners to bring down May's deal in an attempt to destabilize the government and force a new election.
Before the Sun interview was published, May invoked Winston Churchill as she addressed Trump and business leaders at a black-tie dinner at Blenheim Palace, the grand 18th-century country house which was the British World War Two leader's birthplace.
Trump, who is making his first presidential visit to Britain, told the Sun newspaper he had advised May on how to conduct Brexit negotiations, "but she didn't listen to me".
"Now, for the benefit of all our people, let us work together to build a more prosperous future".
Trump arrived at the reception to much pomp and ceremony, with the bands of the Scots, Irish and Welsh Guards playing in his honour.
He then travels north to Scotland where he will spend the weekend privately, joined by son Eric Trump.
There were also demonstrations close to Winfield House, the United States ambassador's residence near Regents Park where the president and first lady Melania Trump will spend the night.
Even if Brussels were to accept some form of today's plan, it now appears unlikely Mrs May has the votes to get it through Parliament.
Mrs May and her husband Philip, joined by around 150 guests, waited outside Blenheim Palace in the sunshine for the president and first lady.
Among the crowd of protesters outside American man Martin Williams, who works at Oxford University, called Mr Trump a dictator.
He said: "I understand that people won't all agree, people have very strong views on the Brexit issue".
"He is destroying all the norms of what used to be a great democracy in America and so I'm really concerned about my country and I'm here now and so this is where I have the chance to protest him".