The UK parliament has authorised Prime Minister Theresa May to reopen negotiations with the European Union to replace a controversial Irish border guarantee within her Brexit deal, in a move that immediately received a flat rejection from Brussels.

Two weeks after resoundingly rejecting the divorce agreement May spent a year and a half negotiating with the bloc, members of parliament on Tuesday backed a proposal intended to send her back to Brussels with a stronger mandate to seek changes that were more likely to win their support.

At the same time, they also passed a non-binding amendment ruling out a potentially chaotic "no-deal" exit.

But they failed to vote through what is seen as a more important plan - backed by European supporters - that would have tried to force through a Brexit delay if no new deal with the EU emerged by February 26.

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With two months left until Britain is due by law to leave the EU - on March 29 - the government is facing increasing calls to secure a deal to allow an orderly exit from the bloc.

"Tonight, a majority of honourable members have said they would support a deal with changes to the backstop," May, leader of the ruling Conservative Party, said.

"It is now clear that there is a route that can secure a substantial and sustainable majority in the house for leaving the EU with a deal," May said, adding she would seek "legally binding changes".

The Irish backstop is an insurance policy that aims to prevent the reintroduction of a hard border between EU member, Ireland and Northern Ireland, which is part of the UK, a crucial part of a 1998 peace deal that ended decades of sectarian violence and preserve frictionless trade.

However, critics said it could bind the United Kingdom to the EU's rules indefinitely.

The proposal put forward by influential Conservative legislator Graham Brady and passed by 317 votes to 301, called for the backstop to be replaced with unspecified "alternative arrangements", and said parliament would support May's Brexit deal if such a change was made.

EU says 'no'

The British pound quickly fell amid fears May would not be able to convince Brussels to reenter negotiations, with Brussels repeatedly saying it does not want to reopen a treaty signed off by the other 27 EU leaders.

Speaking immediately after the vote in parliament, a spokesman for European Council President Donald Tusk said the backstop was part of the withdrawal deal and not up for negotiation, a stance echoed by the Irish government.

"This is a deal which was negotiated with the UK, by the UK, signed off by the UK and the prime minister - and now it looks as though this evening, essentially, there is a row-back and a reneging on the commitments that were made," said Irish European Affairs minister Helen McEntee.

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French President Emmanuel Macron's office said there could be no renegotiation and demanded a "credible" British proposal.

If the British parliament cannot find a majority for a way forward, the UK will leave the largest global trading bloc without any deal, a scenario that businesses fear will bring chaos to the world's fifth-biggest economy.

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Neither May nor her ministers spelt out what compromises she would seek from the EU, but suggestions include securing a time limit to the backstop or allowing a unilateral exit clause - elements that defeat its purpose, according to the EU.

Hardline pro-Brexit Conservative legislators made clear that their support for May on Tuesday was conditional on her securing a deal they approved of.

EU diplomats played down May's chances of being able to present a substantially different deal to the British parliament in a decisive vote expected to take place on February 13.

"May will now come back to Brussels and be rebuffed," one diplomat was quoted as saying by the Reuters news agency. "The House of Commons will have to vote again mid-February on plan C. And it will have to be plan A all over again, but with even more pressure of no-deal Brexit looming."

Al Jazeera's Nadim Baba, reporting from outside the UK parliament in London, said the possibility of Britain seeking a delay in its upcoming exit from the bloc was gathering pace.

"Tuesday was meant to be about parliament giving us an idea of what kind of a deal it would be prepared to back," he said.

"But now we know there'll be weeks more deliberations here, and it's looking more and more likely that the UK will have to ask the EU for extension to Article 50 - buying itself more time," he added, referring to the legal notification for leaving the EU which set in motion a two-year process for Brexit.

UK members of parliament on Tuesday rejected two amendments that set out a clear path for parliament to prevent a no-deal exit if May cannot get a deal passed next month.

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However, they did later approve a symbolic proposal calling on the government to stop a potentially disorderly no-deal exit, sending a signal that a majority oppose such a departure.

It provided no mechanism for preventing a no-deal Brexit but kept open the option that politicians could try to take the initiative in the "amendable" vote that May has promised for February 14 if she cannot get a deal approved.

UK Labour Party leader Jeremy Corbyn said he would meet May to "find a sensible Brexit solution that works for the whole country", listing changes that his party wanted to see, but that May has shown no sign of supporting.

Sterling, which recently hit a two-and-a-half month high of $1.3218 on hopes that a no-deal Brexit would be avoided, fell about 0.8 percent.

"This isn't a good night for the country," Labour legislator Wes Streeting tweeted.

"The prime minister voted against her own deal to go back to Brussels for something she's said is impossible. MPs voted against 'no deal' - but also voted to make 'no deal' more likely. We’ll be back for another round of Groundhog Day soon."