Her divorce deal with the European Union has been defeated three times by the lower house of the British Parliament, which failed on Monday to find a majority of its own for any alternatives.
The Labour leader described the talks as "useful but inconclusive" and said "there has not been as much change as I expected". "The meeting was useful but inconclusive".
The Tory MP is part of a cross-party group of Europhiles intent on stopping a proper, no deal, Brexit, who along with Labour's Yvette Cooper and former Conservative MP Nick Boles threatened a government shutdown in January by attempting to stop the Treasury spending on no deal arrangements.
Former foreign secretary Boris Johnson said: "It is very disappointing that the Cabinet has made a decision to entrust the final handling of Brexit to Jeremy Corbyn and the Labour Party". He himself has said such a vote should be restricted to specific circumstances.
But Barnier said in Brussels on Tuesday, "if the U.K. Still wants to leave the European Union in an orderly manner", Theresa May's deal "is, and will be the only one". "There was no agreement reached on that".
Following the mammoth Cabinet meeting on Tuesday, one source said ministers were split 14-10 against asking for a long extension to the Brexit process.
European Parliament Brexit coordinator Guy Verhofstadt, who had said he thought a no-deal Brexit was "nearly inevitable", welcomed Mrs May's offer of talks with Mr Corbyn.
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May said the extension she would seek beyond the current legal departure day of April 12 should be "as short as possible" without specifying any period, and added that it should end when a deal is ratified by parliament.
European Union officials say it is "very likely" that Britain will depart without a deal, bringing potentially devastating political and economic consequences.
Britain's Prime Minister Theresa May speaks in the Parliament in London, Britain April 3, 2019, in this screen grab taken from video.
He said the bloc was ready to upgrade a proposed blueprint for new EU-UK relations after Brexit from the one already negotiated by May.
May and Corbyn were to face off at the weekly Prime Minister's Questions in the House of Commons ahead of a likely meeting in parliament during the afternoon.
In his letter, Mr Adams said the Government faced two "great challenges" of delivering "the Brexit the people voted for" and preventing a Corbyn premiership.
The EU has repeatedly refused to renegotiate the Brexit divorce deal it agreed with May last November after nearly two years of negotiations but has said it could revise the accompanying political declaration on future relations.
The Prime Minister last night invited the Labour leader for talks as she called for "national unity" to break the deadlock on how the United Kingdom should leave the EU.