The other 27 EU leaders met without May over dinner to thrash out what European Council president Donald Tusk called "a flexible extension until 31 October".
He suggested May's government now had time to ratify the deal agreed with European Union leaders in November, to rethink its approach or to stop the entire Brexit process. "Please do not waste this time", he added, addressing British politicians.
Mrs May said the European Council had reiterated that the Withdrawal Agreement could not be re-opened. "It can also reconsider the whole Brexit strategy ... but not in the withdrawal agreement".
"U27 has agreed an extension of Art. 50".
Tusk had proposed a year-long delay, but said: "It's still enough to find the best possible solution".
The latest extension, being dubbed a "Brextension" and also drawing inevitable Halloween analogies with the date coinciding with the festival celebrating scary and nightmare scenarios, comes just a day before the April 12 deadline from the first extension agreed by the European Union (EU) to the official Brexit Day of March 29.
But senior Conservatives have warned the demands for her to go are only likely to intensify, particularly - as many now expect - the European elections do go ahead.
"A longer Brexit extension would have been better!" tweeted Norbert Roettgen, chairman of the German parliament's foreign affairs committee and a member of Merkel's party. "But it was not logical, in my view - and above all, it was neither good for us nor for the United Kingdom", he said. "But Macron prioritised his own election campaign and interests over European unity".
Mr Macron is concerned that letting Britain stay too long would distract the EU from other issues - notably next month's European Parliament elections.
NBA Playoffs 1st Rd Line Report: Sun April 14
The Slovenian teenager averaged 21.2 points, 7.8 rebounds and 6.0 assists in his first National Basketball Association season. Other short odds to win are the Houston Rockets (+600), the Denver Nuggets (+1400) and the Oklahoma City Thunder (+1400).
Donations pour in for boy thrown from Mall of America balcony
The complaint says Aranda approached a woman who was waiting for the restaurant to open and asked her to buy him something. The woman refused, and Aranda allegedly threw a glass of water in her face and a glass of tea that struck her leg.
Winx racks up 33rd consecutive victory in final race
I mean, she just showed you what she is capable of doing. "It's great for out sport", Waller said. All over Australia". "( Winx ) has captured the hearts of people all around the world".
"The European Council takes note of the commitment by the United Kingdom to act in a constructive and responsible manner throughout the extension period in accordance with the duty of honest cooperation, and expects the United Kingdom to fulfill this commitment and Treaty obligation in a manner that reflects its situation as a withdrawing Member State", the document continues.
Speaking to reporters herself, May later said that key to her agreement was to have an earlier exit clause.
"She said of Wednesday's result that" it may well be a more extension than the one the British prime minister asked for, however we'll shape this extension in such a way that whenever Britain has accepted the withdrawal agreement, Britain can then complete its orderly withdrawal very soon after" using a two-year transition period.
Earlier, May had said that she would step down from her post if she managed to pass her beleaguered deal in the British Parliament.
In a statement to the House of Commons, Mrs May said she "profoundly" regretted her deal not being agreed to by MPs.
The "De Gaulle moment" that many had speculated about before Wednesday night's Brexit summit (10-11 April) did not come, but President Emmanuel Macron still lived up to the spirit of the post-war French leader by throwing his weight around the European Union table.
UK Prime Minister Theresa May has told MPs it remains her "priority" to deliver Brexit, defending the decision to delay the UK's exit from the EU. However, it will be hard for the Brexiteer faction of the Conservatives to push May out before October because, after the failed oust attempt in December, the Prime Minister is immune to a new challenge from within her party until next December.
Every initiative has floundered so far.
A few days of discussions between the Conservative government of May and the opposition Labour Party targeted at finding a compromise have failed to make a breakthrough. Labour favours a softer Brexit than the government has proposed, and wants to retain a close economic relationship with the bloc.