Brussels, Dec 14 (IANS): European Union leaders have refused to give UK's Prime Minister Theresa May a lifeline over Brexit, saying that the withdrawal agreement is "not open for renegotiation", despite her appeal to them to help her salvage the deal by putting a 12-month limit on the unpopular Irish backstop.

May came to Brussels to plead EU leaders on Thursday at a summit to make the agreement more palatable to sceptical lawmakers in London.

But after the meeting, representatives of the bloc said they were sticking with the withdrawal agreement previously agreed with London, including the Northern Ireland backstop deal which threatens to derail it in the UK Parliament.

May delayed a Commons vote on the deal earlier this week when it became clear she would suffer a heavy defeat.

"If we go into negotiations on the future relationship, we need to have a well-constructed proposal and a cogent idea from our British partners and friends, and then we'll look at that," European Commission President Jean-Claude Juncker told reporters.

The UK leader had been seeking legally enforceable guarantees surrounding the Irish backstop -- aimed at preventing the return of a hard border between Northern Ireland and the Republic of Ireland. It has emerged as the crucial sticking point for many in May's Conservative Party, furious that Britain could only leave it with the approval of the EU.

Critics say the backstop would keep the UK tied to EU rules indefinitely and curb its ability to strike trade deals. Conservative MPs demanded changes to the backstop to make it clear that it could not last forever, and Britain could terminate the arrangement on its own.

At the summit, May was seeking legal assurances that the backstop, if used, would be temporary.

"In terms of a no deal, let's not forget ultimately, it is within the gift of the UK government and the UK Parliament to take the threat of no deal off the table," Irish Prime Minister Leo Varadkar said.

"It is possible if the UK wishes to, to revoke Article 50, or, if that's a step too far to seek an extension of Article 50," he added, referring to the piece of EU law by which the UK triggered Brexit.

Speaking after the Brussels summit, European Council President Donald Tusk called the backstop "an insurance policy", saying it was the EU's "firm determination" to work "speedily" on alternative arrangements.

Tusk said the backstop would "apply temporarily unless and until it is superseded by a subsequent agreement that ensures that the hard border is avoided".

The European Council's conclusions on Brexit published on Thursday said that the EU would continue trying to negotiate a trade deal with the UK even if the Irish backstop had been triggered at the end of the transition period.