In an unusual reconciliation letter, May told Corbyn that both parties should discuss how "alternative arrangements" for the Irish backstop – a mechanism to avoid a hard border – can work.
She also said that she was "grateful" to Corbyn to meet her last week, but excluded in the customs union – one of the supervisor's demands to support her business.
Reply to his letter from last week, May wrote: "It is good to see that we agree that the UK should leave the European Union an agreement and that the urgent task is to find an agreement honoring our commitments to the Northern Ireland people , can order support in the Parliament and can be negotiated with the EU – not to seek a election or a second referendum. "
But in an attempt to win over potential labor rebellions, the Prime Minister made a concession on the rights of the environment and workers and rejected the Corbyn's call to full adaptation to the EU but proposes a voting right every time they are changed.
However, the Prime Minister's letter comes into growing concern both inside and outside its cabinet as the prime minister tries to run the clock until March when Britain is scheduled to leave the EU, so Parliament is forced to support its current agreement or leave without any agreement at all.
Some believe the best chance of forcing a vote earlier than March lies with Labor. Shadow Brexit's secretary Keir Starmer said on Sunday that they could table an amendment that would force a vote to be held by February 26 at the latest.
Starner said on Sunday that he believes the prime minister "pretends to make progress" in negotiations with the EU, while "cynically" runs around the clock.
"We can't let that happen," Starner told The Sunday Times.
"It must be a day when Parliament says it's enough."
Meanwhile, Brexit secretary Steve Barclay and EU negotiator Michel Barnier will hold talks in Strasbourg later, with negotiators ready to discuss any changes to the agreement negotiated last year.
The Prime Minister's Brexit deal was rejected with a large margin in Commons last month and she is officially obliged to renegotiate it as soon as possible.
But it is a growing recognition that she will not be able to make any changes until the end of February early.
She resumed talks with the EU last week in an effort to secure concessions the rebel Tory MPs could support, but she is very unlikely to secure the changes in the backstop she is seeking.
EU negotiators, supported by the Member States, refuse to water the Irish backstop, which a majority of MEPs want to see, scrapped completely.
If, as expected, the prime minister does not secure any EU concessions before Wednesday, Parliament will vote on alternative options on Thursday. She will also promise that if she has not renegotiated the agreement at the end of February, MEPs will again be able to vote on what will happen next.
Joint Secretary James Brokenshire confirmed on Sunday that if no revised business members were introduced on February 27, MEPs would again receive an amendment, meaning they could vote on preferred ways forward.
"If the meaningful voice has not happened, in other words, things have not ended, then Parliament would have the additional opportunity by February 27, he says.
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