However, MPs are still expected to debate and vote on amendments to the Brexit deal on Thursday although it will not be known until later what those amendments are likely to be.
MPs and peers, including former ministers Phillip Lee, Sam Gyimah, Guto Bebb and Lord Willetts said her current Brexit deal "risks further dividing our nation and costing jobs" and is "highly unlikely" to benefit families and communities.
Writing her response to his letter of last Wednesday, Mrs May told the Labour leader: "It is good to see that we agree that the United Kingdom should leave the European Union with a deal and that the urgent task at hand is to find a deal that honours our commitments to the people of Northern Ireland, can command support in Parliament and can be negotiated with the EU - not to seek an election or second referendum".
May is set to update parliament on her latest meetings in Brussels and Dublin aimed at securing a divorce agreement with the European Union, with Britain due to leave the bloc on March 29.
This will leave the prime minister having to instead either persuade her MPs and the Democratic Unionist Party to accept a lesser tweak to the backstop, which seems a tough ask, or put together a plan which would win over enough Labour MPs to see her over the line.
"We must agree a deal that this house can support and that is what I am working to achieve", she told the House of Commons.
"She's determined to ensure the right person follows her, and she'll have no say at all if it gets to the stage of forcing her out".
Labour's Brexit policy chief Keir Starmer told the Sunday Times newspaper that his party would seek to use the debate in parliament this week to prevent May from waiting until the last minute to come back with a deal, and compel her to present a fresh accord for lawmakers to consider before February 26.
She added: "Jeremy Corbyn's letter to the Prime Minister this week makes clear our unequivocal opposition to a no-deal Brexit, the Prime Minister's current deal or any tweaked version of it, a CETA style deal or any deal that could lead to a hard border in Northern Ireland".More news: Here Are The Insane Pics Kylie Jenner Posted From Stormi's First Birthday
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Britain is scheduled to leave the bloc on March 29.
She might, for example, get away with some sort of firm European Union assurance on the backstop that does not in fact remove it.
The EU has remained adamant that no changes would be made to the withdrawal agreement, which together with the political declaration is part of the deal the two sides negotiated over 18 painstaking months.
The EU's chief Brexit negotiator Michel Barnier has called for "clarity and movement" from Britain.
She described the possibility of cross-party support for security co-operation as sending "a powerful signal to Brussels".
"This is of huge economic importance to United Kingdom businesses, ensuring continuity for 15,000 British exporters. Not only will this help to support jobs throughout the United Kingdom but it will also be a solid foundation for us to build an even stronger trading relationship with Switzerland as we leave the European Union".
May's thinking, it is suspected, is that by going at a time of her own choosing and in a position of relative strength, she will be able to have some say over who the next Tory leader will be. However, the decisive vote won't come until she has secured changes to the Irish backstop clause.
"It is a negotiation". 'I don't think there is any mileage in trying to do a deal with Labour, ' he told the BBC. British lawmakers overwhelmingly rejected the deal, agreed in November, in a vote last month, leaving Britain on course for an abrupt Brexit with no transition period to minimise expected economic disruption. Figures released Monday showed that Britain's economy slowed past year to its joint-slowest annual rate since 2009, with business investment declining for four straight quarters.