Prime Minister Theresa May told EU leaders Thursday that she could get her Brexit deal through parliament if they gave her the right assurances that it would not "trap" Britain in an indefinite customs union.

The Conservative leader this week postponed a parliamentary vote on the deal in the face of huge opposition among MPs, including in her own party, who promptly launched a confidence vote against her.

Addressing the other 27 European leaders at the Brussels summit, May said the agreement struck with the bloc last month could still pass when MPs vote again in January.

"There is a majority in my parliament who want to leave with a deal," she told them, according to a British official.

"So with the right assurances, this deal can be passed. Indeed it is the only deal that is capable of getting through my parliament."

May said she is seeking "legal and political assurances" over clauses in the text designed to keep the border with Ireland open.

The so-called backstop risks keeping Britain indefinitely in the EU's customs union, something euroskeptic Conservatives and May's Northern Irish allies will not accept.

"We have to change the perception that the backstop could be a trap from which the UK cannot escape. Until we do, the deal – our deal – is at risk," May said.

The official said that May was looking for "political impetus" on Thursday, with the detailed work on what form the assurances could take to be carried out by officials in the weeks ahead.

May warned Britain could fall "accidentally" into a situation where it leaves the EU on March 29 without any agreement.

"It is in none of our interests to run the risk of an accidental no deal with all the disruption that would bring, or to allow this to drag on any further," she said.

EU leaders have warned they will not re-open the Brexit deal, but are looking at "clarifications."

May won the confidence vote on Wednesday but 117 – more than one-third – of her MPs opposed her, suggesting she will struggle to get her party behind her Brexit deal.

"Over the last two years I hope I have shown that you can trust me to do what is right, not always what is easy, however difficult that might be for me politically," she told leaders.

EU offers Britain some Brexit assurances over Brexit backstop

And EU leaders gave May assurances on Thursday that they would seek to agree a new deal with Britain by 2021 so that the contentious Irish backstop is never triggered.

"It is not open for renegotiation," the 27 national leaders said in a joint statement of the tentative Brexit deal they had agreed with May in late November but which the British leader has since taken back to Brussels for more assurances she says she needs to get it passed by her divided parliament.

Ireland blocked a line that had been included in an earlier draft of the EU statement promising Britain that the bloc would look into giving May more assurances later on.

The bloc said it wanted to "establish as close as possible a partnership with the United Kingdom in the future" and would aim to have it in place by the end of 2020 "so that the backstop will not need to be triggered."

If the backstop were triggered, the EU said it would apply "temporarily, unless and until it is superseded by a subsequent agreement" that would ensure no return to a hard border on the island of Ireland.

The bloc promised to undertake its "best endeavors" to ensure the backstop, a fall-back guarantee to avoid a hard border, would only be applied "for as long as strictly necessary."