BRUSSELS   -  The European Union (EU) leaders have made it clear to British Prime Minister Theresa May that renegotiation on the Brexit agreement is a non-starter, Xinhua said on Friday.

European leaders were gathering in Brussels for a customary two-day summit. High on the agenda were Brexit, multi-annual budget and migration.

"The (European) Union stands by this agreement and intends to proceed with its ratification. It is not open for renegotiation," European Council President Donald Tusk said at a midnight press conference following marathon closed-door talks.

Standing by Tusk's side, European Commission President Jean-Claude Juncker echoed, saying: "We can add some clarifications, as Donald was explaining to what has been read upon, but (there) will be no renegotiations."

The summit came on the heels of May surviving a non-confidence vote among her own Conservative MPs, many of whom bristled at May's move to defer a vote on her Brexit deal in parliament. The major hurdle against parliamentary approval is the issue of the so-called backstop, or the border on the Island of Ireland, which has been a sticking point in the painful Britain-EU negotiations on how Britain will leave the regional bloc in March next year.

The storm on the other side of the British Channel was under EU's radar. In an apparent move to assuage concerns of the British parliament, the EU leaders underlined that "the backstop is intended as an insurance policy to prevent hard border on the island of Ireland and ensure the integrity of the Single Market."

British Prime Minister Theresa May insisted Friday that her Brexit deal was still alive and kicking, despite a stinging rebuff from the European Union after she asked for changes to make the agreement more palatable to U.K. lawmakers.

Nonetheless, May told reporters in Brussels that she welcomed the EU's words — and that as formal conclusions of an EU summit, they "have legal status."

"There is work still to do, and we will be holding talks in coming days about how to obtain the further assurances that the U.K. Parliament needs in order to be able to approve the deal," May said.

Diplomats said May had exasperated EU leaders at a meeting on Thursday by failing to outline precise proposals for what she needed to push the deal through, and even at one point used her much-derided mantra of "Brexit means Brexit." "If this is all she has for us, there is no point trying too hard now," one diplomat told Reuters. "She still needs to do her homework — maybe she'll come back in January with something concrete and then we will see. To say 'Brexit means Brexit' more than two years after it all started was what toughened the other leaders' stance," said the diplomat.