Speaking after over seven hours of emergency cabinet talks, May made the announcement after the EU's chief negotiator, Michel Barnier warned that a disruptive and costly Brexit was likely unless Britain broke the impasse that has paralyzed the UK government and Parliament.
After failing repeatedly to win Parliament's backing for her Brexit roadmap, May said the country needed "national unity to deliver the national interest."
Following the defeat of her government's plan and a range of alternatives drafted by MPs, May said Britain would need a further delay to its EU departure, currently scheduled for April 12th, offering to hold talks with opposition Labour Party leader Jeremy Corbyn in an attempt to find a compromise solution.
Reaction from Europe
Following May's televised address from 10 Downing Street, European Council President Donald Tusk gave a cautious welcome to the Prime Minister's change of course. In a tweet following the announcement, Tusk wrote "Even if, after today, we don't know what the end result will be, let us be patient," suggesting the EU would wait for Britain to present a clear plan.
Earlier, EU chief negotiator Michel Barnier offered a downbeat assessment of the situation from Brussels, saying "as things stand now, the no-deal option looks likely. I have to tell you the truth." He added, "we can still hope to avoid it" if London produced a breakthrough before an emergency EU summit scheduled for April 10th
The leaders of the EU's 27 remaining countries have given the U.K. until April 12th to leave the bloc or to come up with a new plan, after British MPs repeatedly rejected an agreement struck between the bloc and May late last year.
Options for the UK
The House of Commons has also failed to find a majority for any alternative plan in two days of voting on multiple options.
May's statement came after a seven-hour meeting of her fractious Cabinet, which is split between supporters of a "soft Brexit" that keeps close economic ties with the EU, and Brexiteers who believe a no-deal exit is better than compromising.
May's words seemed to indicate that she was veering away from the possibility of a no-deal Brexit but also that she has not given up on her own unloved withdrawal agreement.
Her plan is to seek approval for the legally binding agreement which sets out in detail the terms of Britain's departure from the EU after securing cross-party political support for a vision of future ties between the U.K. and the bloc.
If she and opposition Labour leader Jeremy Corbyn fail to reach agreement, May said Parliament would get to vote on a range of options and the government would be bound by the result.
It is the first time she has committed to following the instruction of lawmakers.
May has not indicated how long an extension she would seek from the EU, though she said she hoped Britain could pass the agreement by May 22nd, in time to avoid participating in elections for the European Parliament.
Corbyn open to talks, Brexiteers furious
Meanwhile, Jeremy Corbyn has said he would be "very happy" to sit down with May, even though "so far she hasn't shown much sign of compromise."
He added that Labour would present May with its conditions for Brexit, which include a close economic relationship with the bloc through a customs union, maintaining high environmental standards and protecting workers' rights.
May's move has infuriated pro-Brexit politicians, who say Britain must cut ties to the EU in order to forge an independent economic policy.
Prominent Brexiteer, former Foreign Secretary Boris Johnson commented, "I think people will feel very short-changed."
We cannot avoid failure for them: Macron
Meawnhile, French President Emmanuel Macron said that if Britain's politicians could not agree on a way forward, "they will de facto have chosen for themselves to leave without a deal."
"We cannot avoid failure for them," Macron said before a meeting in Paris with Irish Prime Minister Leo Varadkar.
But Varadkar stressed "there's still time" for May to come to the April 10 summit with "credible" proposals.