LONDON — British Prime Minister Theresa May said Tuesday that she wouldn't agree to a Brexit deal with the European Union "at any cost," as the two sides remained deadlocked on the issue of the Irish border.

May briefed her Cabinet on progress toward an elusive divorce deal with the bloc. Talks are stuck on finding a way to ensure there are no customs posts or other checks along the border between the U.K.'s Northern Ireland and EU member Ireland.

The two sides are working on a proposed solution involving a common customs arrangement for the U.K. and the EU. But May faces pressure from pro-Brexit Cabinet members not to agree to a solution that binds Britain to EU trade rules indefinitely after it leaves the bloc in March.

EU leaders insist that for the "backstop" border guarantee to be effective it must be binding and can't be time-limited.

Irish Prime Minister Leo Varadkar said he was open to "creative solutions" for the border impasse, but "there can be no expiry date and there can be no unilateral exit clause."

"If it were to be either of those things, the backstop would not be worth the paper it was written on," Varadkar told Irish lawmakers.

May spokesman James Slack said the prime minister told Cabinet she was confident of reaching a deal, but added that "while the U.K. should aim to secure a withdrawal agreement as soon as possible, this should not be done at any cost."

He said "there remains a significant amount of work to do."

With Britain due to leave the EU on March 29, May is running out of time to find an agreement that is acceptable both to her divided Conservative government and to fellow EU nations.

Chief EU negotiator Michel Barnier said the two negotiating teams are not yet close to agreement.

"We are not there yet," Barnier tweeted.

Earlier, he told Belgian broadcaster RTBF that "there is still a real point of divergence on the way of guaranteeing peace in Ireland, that there are no borders in Ireland, while protecting the integrity of the single market."