But the European Union said British lawmakers could delay until May 22 if they could come with a deal by next week - but if they couldn't, the exit will happen by April 12.
But now, a May 22 departure date will apply if parliament rallies behind the British prime minister next week.
In the meantime, people are taking matters into their own hands, as a petition requesting to cancel Article 50 has now hit more than two million signatures.
He went straight into a one-on-one meeting with Mrs May who has agreed to the plan.
However, May said it would be "wrong to ask people in the United Kingdom to participate in these elections three years after voting to leave the EU".
Mrs May met European Council president Donald Tusk and Irish Taoiseach Leo Varadkar for one-on-one talks ahead of her presentation. But a longer extension is only possible if the United Kingdom agrees to stand in the European elections in May, the EU's Donald Tusk has said.
"We have done everything we could to get it over the finishing line".
Asked about claims that they had jeopardised MPs" personal safety, a No 10 spokeswoman said: "I flatly reject that'.
"There is no more than we can give", he added.
Firstly I welcome the Council's approval of the legally-binding assurances in relation to the Northern Ireland backstop which I negotiated with President Juncker last week.
Mr Russell-Moyle blamed the Prime Minister for having "whipped up fear and division with her speech last night", while Labour frontbencher Angela Rayner said the incident in Brighton was "terribly worrying". "There is no more that we can have".
"I hope we can all agree, we are now at the moment of decision", May said on the possibly last summit of a British prime minister as a member of the European Union leaders' club.
"Last night I expressed my frustrations and I know that MPs are frustrated too - they have hard jobs to do".
Leave-backing Stewart Jackson, who was David Davis's chief of staff when he was Brexit secretary, said she should "stand down immediately" if she loses next week's vote. Be there in a minute, a week, three weeks, perhaps a year.
Mrs May said she would be doing her utmost to ensure her deal was passed next week.
"Tomorrow morning I will be returning to the United Kingdom and working hard to build support for getting the deal through".
Former UKIP leader Nigel Farage has announced that he will lead his new Brexit Party into the European elections if UK MPs decide to delay Brexit beyond May 22.
May later exited the room, leaving the EU-27 having to decide when the United Kingdom would leave the bloc.
If Mrs May has failed to secure Commons support for her Withdrawal Agreement, this is the final day on which the United Kingdom can set out its next steps to the European Council, if it wishes to be granted a longer extension.
Senior Conservatives are deeply pessimistic that she can win over enough Brexiteer Tories and DUP MPs to secure a majority in the third "meaningful vote" she plans to hold next week on her proposals.
Her comments came after the Commons Deputy Speaker Sir Lindsay Hoyle emailed MPs on Wednesday - before Mrs May's address - advising them to travel by taxi or with colleagues amid heightened tensions in the run-up to next week's votes.
Worn down by three years of indecision in London, European Union leaders on Thursday grudgingly offered the United Kingdom more time to ease itself out of the bloc, delaying by several weeks - but not eliminating - the threat of a chaotic British exit.