London — British Prime Minister Theresa May on Tuesday won a few weeks to salvage a Brexit deal but headed toward a clash with the European Union by promising to overhaul the divorce agreement she spent a year and a half negotiating with the EU. Trying to break the U.K.'s Brexit deadlock, May got Parliament's backing for a bid to rework an Irish border guarantee in the withdrawal deal — a provision May and the EU both approved, and which the bloc insists cannot be changed.

May said she knew there was a "limited appetite" in the EU for changes to the deal, but she believed she could "secure" it, BBC News reports.

The EU said that the current agreement with the U.K. remains the "best and only way" to ensure an orderly Brexit. EU Council President Donald Tusk's office said that the "backstop" on the Irish border, which Britain seeks to renegotiate, is "not open for renegotiation."

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May said Parliament has made its wishes clear and that she will now seek "legally binding" changes to the Brexit withdrawal agreement with the EU.

She spoke after British lawmakers voted to try to renegotiate the Brexit divorce agreement with the EU to remove a contentious Irish border measure. The House of Commons voted 317 to 301 to seek to replace the Irish border "backstop" that keeps the border between Ireland and Northern Ireland free of checkpoints.

The EU did leave other options for negotiation open.

Tusk spokesman Preben Aamann said that "if the U.K.'s intention for the future partnership were to evolve, the EU would be prepared to reconsider its offer and adjust the content and the level of ambition of the political declaration," referring to the political text to complement the legal withdrawal agreement.

Opposition leader Jeremy Corbyn said he will meet with May to discuss their options. He said he looks forward to meeting May to set out the goals of the Labour Party for Britain's future relations with the EU.

Corbyn had for weeks declined to take part in cross-party talks unless May took the "no-deal" scenario off the table.

May's Brexit plan was rejected in dramatic fashion by parliament on January 15 largely due to opposition to the backstop. Now she's hoping a majority of British lawmakers will agree to back it — if it includes a new or altered arrangement to keep the Irish border "soft."

There is a March 29 deadline, when Britain is scheduled to leave the EU with or without a deal, and fears are mounting that an exit without an agreement in place could cause chaos at ports, shortages of food and medicine, and severely damage the British and, to a lesser degree, European economies.

Mrs. May's gamble is that Europe — keen to avoid such a messy "no-deal" Brexit and frustrated by the fact that Britain has failed as yet to speak with one voice on the matter — might give her some new leeway if she presents a plan with solid parliamentary backing.

The mere possibility that Britain could crash out of the union without a deal has been May's greatest leverage in the negotiations with Europe. But she could lose it on Tuesday night. Anti-Brexit lawmakers are set to try and wrest some control over the process.

Brexit amendment votes

Parliament was to vote Tuesday on seven rival amendments, put forward by lawmakers from all parties, which could significantly alter the trajectory of the Brexit process.

May had urged them to support one measure that calls for the current backstop to be replaced with "alternative arrangements" — but the amendment, crafted by members of May's own Conservative Party, wasn't considered likely to pass as pro-Brexit lawmakers believed it would fail to force significant changes to the measure.

At least two other amendments, with a much greater chance of passage, sought to encourage — or even legally compel — the British government to delay the entire Brexit process if no deal is agreed by set points before March 29.

The EU has said it's willing to grant such an extension, which could be a couple years, but only if there is a clear path for negotiations, granted by consensus in London.

"If there is no plan at all for what should then be different, then a delay makes only very limited sense," German Justice Minister Katarina Barley said Tuesday.

Speaking hours before the vote, May beseeched parliament to reject any amendment that would take the prospect of a no-deal Brexit off the table. She said any such amendment would tie "one hand behind my back" when it comes to her negotiating power with Brussels.

She said Britain must avoid presenting Europe with "a cacophony of voices when this house needs to speak as one."