Theresa May has urged Conservative MPs to put aside “personal preferences” and support a Brexit deal in the Commons.
In a letter to all 317 Tory members of Parliament, the prime minister said “history will judge us all” over the handling of Brexit.
It comes after the government suffered a defeat in a vote on its strategy.
Mrs May says in the letter she will return to Brussels to meet European Commission President Jean-Claude Juncker next week.
She will also speak to the leaders of every EU member state over the coming days, she says.
The prime minister is trying to secure changes to the Irish backstop, an insurance policy designed to avoid a hard border between Northern Ireland and the Irish Republic after Brexit.
The plan is widely disliked by members of her party, who fear it will mean the UK will stay closely aligned to the EU for years to come, without Britain being able to end the agreement unilaterally.
Attorney General Geoffrey Cox, who has warned the backstop indefinitely commits the UK to EU customs rules if Brexit trade talks break down, will set out what changes would be needed to remove it in a speech on Tuesday.
Brexit Secretary Stephen Barclay is also due to meet the EU’s chief negotiator Michel Barnier to discuss the controversial policy on Monday.
Mrs May says in her letter the Commons defeat, in which dozens of Conservatives abstained, was “disappointing”.
“I do not underestimate how deeply or how sincerely colleagues hold the views which they do on this important issue – or that we are all motivated by a common desire to do what is best for our country, even if we disagree on the means of doing so,” she writes.
“But I believe that a failure to make the compromises necessary to reach and take through Parliament a withdrawal agreement which delivers on the result of the referendum will let down the people who sent us to represent them and risk the bright future that they all deserve.”
Mrs May says without a withdrawal deal passing in the Commons, Parliament might stop Brexit altogether.
Alternatively, she says the UK might leave without a deal, which would disrupt the economy and damage jobs.
‘No change in tactics’
Analysis by Peter Saull, BBC political reporter
Since Thursday and the 10th defeat in the House of Commons for Theresa May over Brexit, the tensions in the Conservative Party have threatened to boil over.
The war of words has reached ministerial level, with business minister Richard Harrington suggesting some of his pro-Brexit colleagues should join former UKIP leader Nigel Farage’s new party.
Therefore while there’s nothing new in terms of the substance of this letter, it represents a clear attempt by the prime minister to calm things down.
Theresa May is also making it clear she won’t change tactics.
The PM believes the only way to get a deal through the Commons and keep her party together is by securing changes to the backstop, even if the EU shows no sign of budging.
Labour Mayor of Greater Manchester Andy Burnham said the Conservatives could not be united and that Mrs May should have to build cross-party consensus.
“There is no agreement between these people and that’s the prime minister’s failing,” he told Sky News’s Sophy Ridge on Sunday.
“She’s spent all of her efforts trying to do that when actually all along there’s probably a deal that could get through Parliament… with a customs union as part of it, as [Labour leader] Jeremy Corbyn has suggested.”
Meanwhile, campaigners for another referendum on Brexit have said there will be a major protest the weekend before Britain’s scheduled departure date on 29 March.