Speaking after seven hours of talks the Prime Minister offered to meet Jeremy Corbyn to come up with a plan for Brexit.
The UK had been due to leave the European Union on March 29 but following a failure to reach a deal Brexit was delayed until April 12.
But on April 2 the Prime Minister told the nation she was requesting a further extension of Article 50.
Cabinet ministers arrived at Number 10 at around 9am for what was originally due to be a five-hour meeting.
Mrs May said she hoped to agree a deal with Mr Corbyn which could be put to the Commons for approval before the April 10 European Council summit, but, if that cannot be achieved, then a number of alternative options could be put to the vote.
Insisting that any resolution should take the UK out of the EU by May 22, Mrs May said: “This is a decisive moment in the story of these islands and it will require national unity to deliver the national interest.”
Mrs May said: “I have always been clear that we could make a success of no-deal in the long term but leaving with a deal is the best solution.
“So we will need a further extension of Article 50 – one that is as short as possible and which ends when we pass a deal.
“And we need to be clear what such an extension is for: to ensure we leave in a timely and orderly way.
“This debate, this division, cannot drag on much longer.”
She added: “Today I’m taking action to break the logjam.
“I’m offering to sit down with the leader of the opposition and try to agree a plan that we would both stick to to ensure we leave the EU and we do so with a deal.
“Any plan would have to agree the current Withdrawal Agreement – it has already been negotiated with the 27 other members and the EU has repeatedly said it cannot and will not be re-opened.”
However, if Article 50 is to be extended this must be approved by the EU.
Even if, after today, we don’t know what the end result will be, let us be patient. #Brexit
— Donald Tusk (@eucopresident) April 2, 2019
Mr Corbyn said: “We will meet the Prime Minister.
“We recognise that she has made a move, 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.”
The move comes as a blow for Brexiteers as by agreeing to work with Mr Corbyn, Mrs May appears to be pursuing a soft Brexit.
Jacob Rees-Mogg, chairman of the pro-Brexit European Research Group, said: “This approach to Government is an unsuccessful one and it also lacks democratic legitimacy.
“People did not vote for a Corbyn-May coalition Government – they voted for a Conservative Government, which became a confidence and supply with the DUP.
“This is a deeply unsatisfactory approach.
“It’s not in the interests of the country, it fails to deliver on the referendum result and history doesn’t bode well for it.”
Mr Rees-Mogg criticised the Prime Minister for planning to collaborate with “a known Marxist” and said the move would lose Tory votes.
He said: “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.”
President of the EU, Donald Tusk, took to Twitter and called for patience in the process.
Speaking to the BBC Hilary Benn said there were a number of important questions – mainly the length of the extension – if the offer of cross-party collaboration is accepted.
SNP leader Nicola Sturgeon said the move could be ‘a trap’.
This thread highlights a massive danger – if MPs allow 12 April to pass with no commitment to fight Euro elections, May 22 becomes the inescapable exit day…and PM would then be able to say it’s my deal or no deal. Parliament needs to be very wary about a potential trap. https://t.co/Z8D7gnbCtJ
— Nicola Sturgeon (@NicolaSturgeon) April 2, 2019
In a post on Twitter she said: “If MPs allow 12 April to pass with no commitment to fight Euro elections, May 22 becomes the inescapable exit day…and PM would then be able to say it’s my deal or no deal.
“Parliament needs to be very wary about a potential trap.”
Labour MP Anna Turley, a leading supporter of the People’s Vote campaign for a second referendum, said that Mrs May was “trying to dip Jeremy Corbyn’s hands into the mess of Brexit”.
But she said that “a deal based on a backroom pact between the Government and the Opposition would simply be a stitch-up that left the people behind”.
Ms Turley said: “Any extension to the Brexit deadline and consideration of other forms of Brexit must be inclusive of all those MPs and voters who say a final deal should be signed off by the people.
“The public will not stand for a Westminster stitch-up. Nor will any deal that was cobbled together in a hurry to meet another artificial deadline command a stable majority in either Parliament or the country for long. It would be a bad deal for Britain if it was made in haste for the wrong reasons.”