Theresa May will sit down with Jeremy Corbyn to agree a Brexit deal that can command the support of the house.
Speaking in Downing Street, the Prime Minister said "national unity" was required to "break the logjam" before May 22.
Mrs May added she was not willing to take the country into a no-deal Brexit on April 12, and would therefore seek another extension to Article 50 to ensure we a "timely and ordely" Brexit.
Mrs May said: "We can and must find the compromises that will deliver what the British people voted for.
"This is a decisive moment in the story of these islands and it requires national unity to deliver the national interest."
Mr Corbyn confirmed his party will meet with the Prime Minister and said he "recognised that she has made a move".
He added: "I recognise my responsibility to represent the people that supported Labour in the last election and the people who didn't support Labour but nevertheless want certainty and security for their own future and that's the basis on which we will meet her and we will have those discussions."
Mrs May said any compromise deal must include her withdrawal agreement, as the EU have "repeatedly said it cannot and will not be re-opened".
If agreement could not be reached, Mrs May said a number of alternative votes could be put to the vote "to determine which course to pursue".
She added: "Crucially the Government stands ready to abide by the decision of the House but to make this process work the Opposition would need to agree to this too."
Speaking to talkRADIO, Change UK MP Mike Gapes said the offer of negotiations could be a "poisoned chalice" for Jeremy Corbyn.
He added: "At the same time, it is a test of him, does he keep to Labour Party policy of insisting that there should be a People's Vote or does he just agree to go along with a customs union which the Prime Minister seems to be moving towards?"
Mrs May's announcement has been condemned by Brexiteers within her own party, with ERG Chair Jacob Rees-Mogg accusing her of collaborating with a "known Marxist".
He aded: "You do find that leaders who decide to go with the opposition rather than their own party find their own party doesn't plainly follow.
"I'm not sure this is the way to conciliate people to persuade them if they haven't moved already to move at this stage.
"I think getting the support of a known Marxist is not likely to instil confidence in Conservatives."