A letter signed by 170 of the 330 Conservative lawmakers in parliament, including 10 cabinet ministers, was sent to May after her Brexit deal was rejected for a third time by the House of Commons on Friday, the newspaper reported.
He stressed President Trump's commitment to Brexit, that he is "eager for the will of the British people to be carried out, and he is even more eager to do a trade deal".
Former Brexit minister Dominic Raab said Friday morning he would vote for the government's Withdrawal Agreement to avoid the risk of Britain having to seek a longer delay to its exit from the EU.
In an editorial, the New York Times tells its readers that while the "indefatigable" prime minister's deal was rejected for a third time "there's still hope a solution can be found". Chaos and uncertainty remain in the country.
May's authority lies in tatters after weeks of turmoil, but officials have hinted she might yet try to bring the deal back to MPs for a fourth and final time.
Within minutes of the vote, European Council President and summit chair Donald Tusk said EU leaders would meet on April 10 to discuss Britain's departure from the bloc. Friday's majority was 58.
In Brussels, the European Commission, the EU's executive branch, said it regrets the negative vote in the House of Commons and now the default Brexit date is April 12.
The next deadline is April 12 to get a deal with the EU.
But 34 Tories still rebelled, and Northern Ireland's DUP stood firm against it because of concerns about the Irish border backstop.
The Daily Mail, another newspaper that supported Brexit, described parliament's decision to vote against May's plans as "The Brexit Betrayal" on its front page.
"Parliament will continue this process on Monday and we need to look at all the options", he said.
Labour leader Jeremy Corbyn called for her to resign and call an election. The opposition leader's remarks in the parliament were echoed by MPs from other parties.
Any new approach at this point would likely require a much longer extension that would force Britain to take part in European Parliament elections in May.
The original Brexit day of March 29 was meant to avoid the British participation in the coming elections.
March 29th is here, a day that should have meant the United Kingdom leave the EU.
Anti-Brexit protesters stand outside the Houses of Parliament in London, Britain, March 27, 2019. "Yet they're on track to deliver either the most disruptive form of Brexit possible, or no Brexit at all".
A second round of indicative votes is expected on Monday with MPs able to submit their options to speaker John Bercow who will then select the options to be debated and voted on. It must either cancel Brexit, seek a longer delay or leave the European Union bloc without a deal.
The prime minister separated her Brexit deal from the 26-page political declaration on future relations when seeking the parliamentary vote partly to meet the recent ruling of Commons Speaker John Bercow that the same motion cannot be tabled twice in the same parliamentary session.