It ramps up the pressure on the embattled prime minister as she considers a last-ditch attempt to save her Brexit deal after suffering a third defeat in the Commons.
One of the MPs who signed the letter said it was two paragraphs long and called on her not to move towards adopting a customs union.
A Conservative source said: “The letter reaffirmed our commitment to the manifesto, and to the PM’s own determination to seek a short extension to Article 50 that avoids the EU elections.”
Mrs May is weighing up her next steps after her deal was voted down by 286 votes to 344 on Friday – the day Britain was meant to have left the EU.
She said the implications of the vote were “grave”, adding: “I fear we are reaching the limits of this process in this House”.
The prime minister has been urged by some in her own cabinet to embrace a no-deal Brexit.
Sky News political editor Faisal Islam said a delegation of ministers went to Downing Street after the vote to urge the PM to reject a softer Brexit and go for no-deal.
Downing Street sources have suggested the prime minister has not given up hope of getting it through the Commons, pointing out that the scale of the defeat was significantly smaller than in the previous two votes.
The government must now present a new way forward to the EU by 12 April or face leaving without a deal on that date.
MPs will consider further options through a series of indicative votes in parliament next week.
Options include remaining in a customs union, holding a second referendum, or no deal.
The EU has called an emergency summit on 10 April to discuss the implications of the vote.
Mrs May said Friday’s vote means Britons will “almost certainly” have to elect MEPs to the European Parliament in elections taking place at the end of May.
After the vote, the PM’s official spokesman refused to deny four times that she is now considering a general election.
Labour leader Jeremy Corbyn said he backed that idea and called for Mrs May to quit.
“The House has been clear this deal now has to change,” he said. “There has to be an alternative found.
“If the prime minister can’t accept that then she must go. Not at an indeterminate date in the future, but now, so that we can decide the future of this country through a general election.”
Meanwhile, Labour deputy leader Tom Watson has suggested the time has come for a national unity government.
In an interview with Prospect magazine, he said: “I prefer Labour governments and I hope we never get to a point where our economy or security is so in peril that we get a government of national unity.”
But he added: “If needs must, we have to then do what’s right.”
Catherine Barnard, professor of European law at Cambridge University, said the PM was “severely weakened”, but told Sky News: “The reality is that nobody actually wants the poisoned chalice at this moment in time.
“There’s lots of jockeying for position going forward once the deal has been done and once we have left, but nobody wants to carry the can at the moment.
“I think it’s very telling that the Article 50 withdrawal agreement is increasingly called Theresa May’s deal so it makes it clear exactly where the blame lies when things go wrong.”