Theresa May is meeting European leaders and EU officials on Tuesday for talks aimed at rescuing her Brexit deal.
She is holding talks with Dutch PM Mark Rutte and Germany’s Angela Merkel after postponing a Commons vote on the deal.
The UK PM has said she needs “further assurances” about the Northern Ireland border plan to get backing from MPs.
European Commission President Jean-Claude Juncker said the EU would not “renegotiate” the deal but there was room for “further clarifications”.
The prime minister is understood to be seeking legal guarantees that the UK will not be trapped in the Northern Ireland backstop plan indefinitely.
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Critics object to the backstop – a temporary customs arrangement designed to prevent the need for checkpoints at the Irish border if a long-term solution that avoids them cannot be agreed – because it imposes different regulations in Northern Ireland from the rest of the UK.
They also object to the fact that under the terms of the withdrawal agreement, the UK can not exit the backstop without the EU agreeing.
Commons leader Andrea Leadsom said Mrs May was seeking to give the UK Parliament a vote on whether to enter the backstop – and an annual vote on whether the country should remain in it.
She told BBC Radio 4’s Today programme this could be done in an “addendum” to the withdrawal agreement, without changing the main text of it.
Asked if this would be enough to satisfy critics of her deal, she said Mrs May was “absolutely determined to get a deal Parliament can vote for”.
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Former Prime Minister David Cameron insisted he had no regrets about calling the referendum, saying he had “made a promise” to do so
The Brexit secretary said policy “had not changed” despite a European court ruling the UK could cancel Brexit without permission from the other 27 EU members
MPs have to give the go-ahead for Mrs May’s deal if it is to come into effect when the UK leaves the EU on 29 March.
Downing Street has said a Commons vote will be held on the deal before 21 January and Brexit minister Robin Walker told MPs he hoped “it would be sooner than that”.
Mrs Leadsom earlier suggested talks with the EU could go right down to the wire, saying: “The EU is always in a position where it negotiates at the last possible moment.”
Jean-Claude Juncker, who will later hold talks with Mrs May in Brussels, said: “The deal that we have achieved is the best deal possible, it is the only deal possible.”
But he said there was “room enough to give further clarifications and further interpretations”.
It is not clear if that would be enough to win over Conservative Brexiteers and the Democratic Unionist Party, whose votes Mrs May relies on to win key votes in the Commons, who have called for the entire backstop plan to be dropped.
Andrea Leadsom said the prime minister had decided to pull the vote on her Brexit deal “at the last minute” after speaking to cabinet members on Monday morning on the phone.
Her U-turn sparked anger among MPs, who had spent three days debating the deal and had been promised the final say on it on Tuesday.
Labour leader Jeremy Corbyn said Mrs May had “lost control of events” and a number of Tory MPs called for her stand down, saying she had lost all credibility.
More backbench Tory MPs are considering submitting letters of no confidence in Theresa May in the hope of toppling her and forcing a Tory leadership contest. If she was no longer Conservative Party leader she would also be expected to step down as prime minister.
So far 26 MPs have publicly said they have written such letters – 48 of them are needed to trigger a vote.
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Former Brexit minister Steve Baker told BBC Radio 4’s Today programme: “It is a grave decision to make, but what I would say to my colleagues is: you now face the certainty of failure with Theresa May, you must be brave and make the right decision to change prime minister.”
Separately, Labour is coming under pressure from the SNP, Lib Dems, Plaid Cymru and the Green Party to call a vote of no confidence among all MPs to try and bring down Theresa May’s government – something that can only be done by the main opposition party.
The four parties want Labour to get behind their campaign for another EU referendum, something Jeremy Corbyn has said could happen if Labour fails in its main objective of forcing a general election.
But Mr Corbyn says he will not table a no confidence motion at this stage because it will stand more chance of success when Theresa May returns to the Commons to put her deal to the vote, which Labour expects her to lose.
However, Labour will seek to keep the pressure on the PM in an emergency debate in the Commons later on Tuesday – which was granted after the decision to call off the vote on the Brexit deal.