Key legislation to ratify the Prime Minister's Brexit deal in law will be brought before the Commons at the beginning of next month, Downing Street has announced.
The Government will bring forward the Withdrawal Agreement Bill in the week beginning June 3, a spokesman said, after Theresa May and Jeremy Corbyn held fresh talks on Tuesday evening.
Mrs May was 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".
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."
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.
"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."
It is understood that Mr Corbyn rejected any suggestion that Labour would support the Withdrawal Agreement Bill without agreement.
DUP Westminster leader Nigel Dodds said it was "highly likely" that Mrs May's deal would be defeated again unless the PM can "demonstrate something new that addresses the problem of the backstop".
He said: "The Prime Minister has not pursued the one option that has ever achieved a positive vote for something in Parliament. Alternative arrangements to the backstop won easily whilst everything else has failed.
"For the Bill to have any prospect of success then there must be real change to protect the economic and constitutional integrity of the United Kingdom and deliver Brexit."
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 Theresa 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 and 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".
The Withdrawal Agreement will go before the Commons in the same week US President Donald Trump is due to make a state visit to the UK.
Mr Trump and his wife Melania will be in the UK from Monday June 3 to Wednesday June 5.
On Thursday June 6, a by-election will be held in Peterborough to find a replacement for MP Fiona Onasanya, who lost her seat through a recall petition after serving time in prison for lying about a speeding offence.