May won the ballot of Conservative MPs on whether she should remain their party leader, by 200 votes to 117. But in a last-minute pre-vote move, she offered a promise to her MPs that she would step down before the next election, which is due in 2022.
Attention now turns to Brussels and the two-day summit.
As the summit got underway, European Council President Donald Tusk said that the EU is willing to help May win the UK Parliament's approval of the Brexit deal.
RELATED CONTENT
"Long and frank discussion with PM Theresa May ahead of Brexit summit. Clear that EU 27 wants to help. The question is how," Tusk tweeted before hosting all EU leaders.
May is seeking legally-binding pledges from EU leaders on the "backstop" - the plan to avoid a return to a manned Northern Ireland border.
Critics say the plan will keep the UK tied to EU rules indefinitely and curb its ability to strike trade deals.
The EU, for its part, says it will not renegotiate the backstop but may agree to greater assurances on its temporary nature.
“The EU27 need to send two clear messages from the summit: that they are united in defending EU principles, and that the UK would find an open door if the British people were to revise their decision [on Brexit]” Ska Keller MEP
It seems unlikely that would win enough support for her Brexit plan to have a realistic chance of getting through the House of Commons, with tensions heightened in the Conservative Party in the wake of Wednesday evening's vote.
European Commission President Jean Claude Juncker said in a phone call with Irish Prime Minister Leo Varadkar on Wednesday that the deal on the table was "a balanced compromise and the best outcome available", and "cannot be reopened or contradicted".
Speaking ahead of the summit, Ska Keller, a German MEP and leader of the Greens/EFA Group in the European Parliament, told this website, "On Brexit, it is clear that there cannot be a change in the Withdrawal Agreement. The EU 27 need to send two clear messages from the summit: that they are united in defending EU principles, and that the UK would find an open door if the British people were to revise their decision [on Brexit].”
Further comment came from Alde leader Guy Verhofstadt who, referring to the delayed UK parliamentary vote on the Brexit deal, said: “It’s time they make up their mind.”
“I can’t follow anymore. After two years of negotiations, the Tory government wants to delay the vote. Just keep in mind that we will never let the Irish down. This delay will further aggravate the uncertainty for people and businesses,” added Verhofstadt, who chairs Parliament’s Brexit steering group.
Theresa May, when asked about a possible date for a rescheduled parliamentary vote, said: "We're just at the start of the negotiations and the start of the discussions."
Meanwhile, the assembly’s Conference of Presidents - or group leaders - have said that the Withdrawal Agreement is “fair and balanced and the only deal possible”, adding, “it is therefore one not open to renegotiation.”
“After two years of negotiations, the Tory government wants to delay the vote … This delay will further aggravate the uncertainty for people and businesses” Guy Verhofstadt
The Conference, together with the Brexit Steering Group, discussed the state of play of the UK’s withdrawal from the European Union on Thursday.
“The Withdrawal Agreement and Political Declaration are the only deal possible. Given EU principles, current UK red lines and the commitments set out in the Good Friday Agreement, [they are] the only deal possible to ensure an orderly withdrawal from the European Union,” the Conference said in a statement.
The statement stressed that renegotiating the backstop was not possible “since it is the guarantee that in whatever circumstances there could be no hardening of the border on the island of Ireland.”
It reiterated that without a backstop Parliament would not give its consent to the Withdrawal Agreement.
The Conference also reiterated its support for as close as possible future EU-UK relationship, such that the deployment of the backstop “would not be necessary.
It reaffirmed that the backstop is “in any case to be used only as a measure of last resort.”
“There will be no transition period without ratification of the Withdrawal Agreement,” it said, adding, “Failure to ratify the Withdrawal Agreement would mean no transition period following the exit from the EU.”
The statement also calls on the European Commission and member states to continue and intensify their work on planning for a No Deal scenario.