Updated 10.10pm with EU reaction - British Prime Minister Theresa May was given a mandate by lawmakers on Tuesday to seek changes from the European Union to the deal for Britain’s withdrawal from the bloc.
But the European Union in a swift response said the deal between Britain and the other 27 EU members is "not open for renegotiation".
"We continue to urge the UK Government to clarify its intentions with respect to the next steps as soon as possible," a spokesman for EU Council president Donald Tusk said.
The Brexit deal was heavily defeated by the Commons earlier this month, with opposition by both Brexit hardliners and Remainers.
The members of the House of Commons voted for a proposal moved by the most senior backbencher in the ruling Conservative Party for the ‘backstop arrangement’ in the Brexit deal to be substituted by ‘alternative arrangements’.
There were 317 votes in favour of the proposal and 301 against.
Brexit hardliners have consistently opposed the backstop, which could see Britain indefinitely tied to EU trade rules in order to keep open the border with the Republic of Ireland.
The proposal backed by the prime minister calls for the backstop to be replaced with "alternative arrangements to avoid a hard border".
Most of the Brexit hardliners backed the new proposal on Tuesday.
May promised before Tuesday’s vote that she would seek a "significant and legally binding change to the withdrawal agreement" with the EU before Britain leaves the bloc as planned on March 29.
Speaking after a phone call with European Commission President Jean-Claude Juncker, she acknowledged the opposition in Brussels to reopening the deal and said it "will not be easy".
"We have the chance to show the European Union what it will take to get a deal through this House of Commons. What it will take to move beyond the confusion, division and uncertainty that now hangs over us," she said.
French President Emmanuel Macron said while attending a meeting of Mediterranean EU countries in Cyprus that the Brexit deal was the "best agreement possible and is not renegotiable".
He urged the British government to "promptly" lay out to EU chief negotiator Michel Barnier "the next steps that will prevent an exit without an agreement, which nobody wants but for which we must all prepare ourselves".
Earlier on Tuesday, the UK MPs defeated a proposal by an Opposition Labour MP for Britain’s departure from the EU to be delayed by up to nine months if no agreement on the terms of the withdrawal deal was reached by February 26.
A proposal which would have held open the possibility of a second referendum was defeated but the MPs voted with a majority of eight in favour of a non-binding motion for Britain not to leave the EU without a deal.
Corbyn agrees to meet May to discuss possible EU deal
Following Tuesday's votes, Opposition leader Jeremy Corbyn accepted an invitation from the prime minister to meet, saying he was doing so since MPs had voted against a no-deal exit.