Downing Street announced legislation to ratify the Prime Minister's Brexit deal in law will be brought back to MPs at the beginning of next month.
Labour and the Tories have been locked in talks for weeks to try and break the political paralysis gripping Westminster.
Brexit has been delayed until October 31 as MPs failed to reach an agreement on how best to exit the EU.
May reached out to Corbyn across the Commons despite fury from many of her hard Brexit backbenchers.
The two sides have now held "useful and constructive" talks as the Government announced a new vote on May's agreement set to be prepared for June 3.
The PM is said to have made clear to the Labour leader that she wanted to bring cross-party discussions to a conclusion and "deliver on the referendum result".
“Because both of us will be crucified by our base if we went into a general election having promised that we would respect the referendum result”
Foreign secretary Jeremy Hunt
A Downing Street spokesman said: "This evening the Prime Minister met the Leader of the Opposition in the House of Commons to make clear our determination to bring the talks to a conclusion and deliver on the referendum result to leave the EU.
"We will therefore be bringing forward the Withdrawal Agreement Bill in the week beginning the 3rd June.
"It is imperative we do so then if the UK is to leave the EU before the summer parliamentary recess.
"Talks this evening between the Prime Minister and the Leader of the Opposition were both useful and constructive.
"Tomorrow talks will continue at an official level as we seek the stable majority in Parliament that will ensure the safe passage of the Withdrawal Agreement Bill and the UK's swift exit from the EU."
'USEFUL AND CONSTRUCTIVE': Downing Street hinted talks were going well between May and Corbyn (Pic: PA)
A Labour Party spokeswoman said Mr Corbyn set out the shadow Cabinet's concerns about the Prime Minister's ability to deliver on any compromise agreement during the talks in Parliament on Tuesday evening.
"In particular he raised doubts over the credibility of Government commitments following statements by Conservative MPs and Cabinet ministers seeking to replace the Prime Minister," they added.
"Jeremy Corbyn made clear the need for further movement from the government, including on entrenchment of any commitments.
"The Prime Minister's team agreed to bring back documentation and further proposals tomorrow."
HOLDING ALL THE CARDS: Jeremy Corbyn and Labour may allow the PM to get a deal on Brexit (Pic: REUTERS)
After a marathon Cabinet meeting earlier on Tuesday, ministers agreed to continue the cross-party efforts to break the impasse but stressed it was "imperative" for a Brexit deal to get through Parliament by the summer recess.
With May's future linked to the passage of a Brexit deal, getting legislation through the Commons and Lords by the summer break could also pave the way for her departure from Number 10.
Ministers spent more than two hours discussing the Brexit situation.
Despite the apparent lack of progress in talks with Labour decided the process should continue, but with a clear view that "we need to get a move on".
Rebels within the party continue to move against May – with many already looking for a successor as they demand she step down sooner rather than later.
DIVIDED: Britain remains split following the EU referendum in June 2016 (Pic: GETTY)
Earlier today, a Cabinet source said Mrs May stressed the need for compromise and said the Government could not give in to "absolutism".
Allies of the Prime Minister attempted to calm Tory fears about the prospect of a damaging split in the party over a customs union – Labour's key demand in the talks.
The Prime Minister was warned by senior Conservatives that she risks losing the "loyal middle" of the Tory party if she gives ground on the issue.
Number 10 sources insisted the Government would not sign up to a "permanent" customs union and any compromise position may only be an "interim" measure.
Some 13 former ministers, together with the chairman of the backbench 1922 Committee, Sir Graham Brady, have written to the Prime Minister urging her not to concede Labour's key demand.
WIPEOUT: Jeremy Hunt warned both parties will be 'crucified' if they don't deliver Brexit (Pic: EPA) Related Articles
SCRAP IT: David Davis urged Theresa May to cut off talks with Jeremy Corbyn (Pic: GETTY)
Foreign Secretary Jeremy Hunt said both the Tories and Labour would be "crucified' by voters if they fail to resolve and respect the referendum result.
The Cabinet minister insisted Britain does not need another referendum or general election.
Referring to cross-party talks, Mr Hunt said: "There is potential because when you look at the fundamentals it is actually in both parties' interests to resolve .
"Because both of us will be crucified by our base if we went into a general election having promised that we would respRead More – Source[contf] [contfnew]