EU leaders have agreed on a plan to delay the Article 50 process, postponing Brexit beyond 29 March.
The UK will be offered a delay until 22 May, if MPs approve the withdrawal deal negotiated with the EU next week.
If they do not, the EU will back a shorter delay until 12 April, allowing the UK time to get the deal through or to “indicate a way forward”.
Mrs May said there was now a “clear choice” facing UK MPs, who could vote for a third time on her deal next week.
They could back the withdrawal deal, deliver on the referendum and leave the EU in “an orderly manner” or face the prospect of having to stand candidates in the European Parliamentary elections, three years after the UK voted to leave the EU.
She said she would be “working hard to build support for getting the deal through”. She said she had “expressed frustration” in her speech last night, in which she blamed MPs for the delay, but added “I know that MPs are frustrated too” and she was “very grateful” to those who had supported the deal.
“I will make every effort to make sure we can leave with a deal and move our country forward,” she said.
She also dismissed calls to revoke Article 50 – as a petition calling for that on the Parliament website attracted more than two million signatures – saying people had voted to leave and were told their decision would be respected.
In a press conference with European Commission President Jean-Claude Juncker, European Council President Donald Tusk said that, until 12 April – by when the UK would have to indicate whether it would stand candidates in the 2019 European Parliament elections – “all options remain on the table … the UK government will still have a chance of a deal, no deal, a long extension or revoking Article 50”. Read more