But with the exit backers in the party in revolt, Conservative insiders predicted further resignations unless and until May drops her plan.
Meanwhile, First Lady Melania Trump played bowls with the Prime Minister's husband.
May has said she will fight off any attempt to unseat her.
Trump told The Sun newspaper that May's plan for Brexit had probably killed off the chance of a U.S.
"Now I see this woman, the Prime Minister, trying to overturn all of our achievements". He blamed "fake news", falsely claiming the report - in a right-wing, pro-Brexit, Murdoch-owned tabloid - had omitted any praise of May.
"But personally, I don't think we should have been rolling out the red carpet for Donald Trump".
He also used the news conference to lay out an ambitious agenda for his Monday meeting in Helsinki with President Vladimir Putin of Russian Federation, saying he had low expectations but high hopes for progress on nuclear arms control issues, Syria and Ukraine.
Asked if May should stay in power, Trump said "that's up to the people".
"I get along with her very well, I have a very good relationship", he said.
The trans-Atlantic relationship has had some awkward moments since Trump's election. "If you actually look at the timeline between Eurodollar's slide and sterling's slide, the two are very much going hand-in-hand", said Alan Ruskin, global head of currency strategy at Deutsche Bank.
Johnson's decision is a hammer blow to the prime minister just days after she received the formal backing of her Cabinet for a controversial new Brexit plan that would tie the U.K.to European Union rules and regulations on goods and agricultural products in perpetuity after Brexit. He said he still believed May should follow his advice. "At some point, she can do what I suggested".
Trump wouldn't say whether he considered Putin a friend or foe, calling him only a "competitor". "The prime minister thanks Boris for his work".
"The question of a leadership challenge, I think it's out the window, gone", said Robert Buckland, Solicitor General for England and Wales.
Trump also said that he stood by his praise of Johnson.
Speaking as he prepared to depart for a European trip in which he will meet the Prime Minister at the North Atlantic Treaty Organisation summit in Brussels before his first visit to the United Kingdom as U.S. president, Mr Trump insisted he got along with Mrs May "very well". I think he's got what it takes'.
Mrs May hailed the meeting as a success but less than 48 hours later she lost key members of Government as David Davis and Boris Johnson quit, stating the paper did not meet the demands of Leave campaigners. "A great job, and I mean that".