In an about-face that left pro-Brexit members of May's Conservative Party howling with outrage, the prime minister sought to forge an agreement with left-wing Labour Party leader Jeremy Corbyn after failing three times to win Parliament's backing for her Brexit deal. The bloc says it will only agree to delay Brexit if Britain breaks its impasse and comes up with a new plan.
It is the latest twist in a saga that leaves Britain, the world's fifth-largest economy, struggling to find a way to honour a 2016 referendum vote to take the country out of the globe's largest trading bloc.
European leaders are considering Mrs May's request for another delay to Brexit, with a decision expected at Wednesday's emergency summit in Brussels.
An extension requires unanimous approval from the 27 remaining national leaders, some of whom are fed up with Brexit uncertainty and reluctant to prolong it further.
Before the European Union potentially agrees a longer delay to Brexit it must weight up the possibility of a future, post-May government being an obstructive member of the bloc.
British Foreign Secretary Jeremy Hunt urged European leaders to be co-operative, saying May "is totally and utterly determined to deliver Brexit".
"Most of the colleagues that I am talking to accept that we will need longer to complete this process, so I am optimistic about the council on Wednesday", he said.
Irish Prime Minister Leo Varadkar said he was "open to extending the deadline". An official in the French president's office said the British leader hadn't offered "sufficient guarantees" to justify a long extension.
German Chancellor Angela Merkel said she would work "until the last hour" to secure an orderly Brexit, but stressed that "these solutions have to be reached above all in Britain itself". The two main parties, parliament and the nation at large remain profoundly split over the terms for departure, or even over whether to leave at all.
However, Parliament has rejected May's Brexit deal with all the European Union three times, amid resistance from pro-EU along with pro-Brexit lawmakers.
Downing Street has insisted it is prepared to pursue alterations to its Brexit deal and is ready to hold further talks with Labour this weekend.
But three days of talks ended without agreement on Friday, with Labour's Sir Keir Starmer saying ministers were not "countenancing any change" to the text. "We are looking for movement".
The UK is now scheduled to leave the European Union on April 12, with British legislators' failure to agree on any scheme for exiting the 28-member bloc raising the possibility of a so-called "no-deal" departure - something May and her European Union counterparts are keen to avoid.
Labour says it has had no indication the government will agree to its demand for changes to the political declaration - the section of Mrs May's Brexit deal which outlines the basis for future UK-EU relations.
It was unclear whether the cross-party talks in London would succeed.
May now is asking for Britain's departure to be pushed back until June 30, hoping to reach a compromise with Labour and a deal through parliament in a matter of weeks.
The Bill, brought forward by backbenchers including Labour's Yvette Cooper, allows Parliament to determine the length of any Brexit extension the Prime Minister should request at the European Union summit on April 10.
May said in her letter that the "impasse can not be allowed to continue", as it was "creating uncertainty and doing damage to faith in politics" in Britain.
The embattled leader opened negotiations this week with the Labour Party in a bid to end months of political crisis over her divorce deal struck with European leaders past year but repeatedly rejected by MPs.
A deal with Corbyn could be May's last chance to deliver Brexit without either a long delay or leaving with no deal at all.