Theresa May says she “is talking to colleagues” about their concerns over the Northern Ireland “backstop” ahead of a crucial vote on her EU deal.
She suggested MPs could be “given a role” in deciding whether to activate the backstop, which is designed to stop the return of a physical border.
But she told the BBC there could be no deal with the EU without it.
No 10 has said the Commons vote will go ahead on Tuesday, despite claims it could be delayed to avoid defeat.
And in another development, the European Court of Justice said it would deliver a ruling on Monday on whether the UK could unilaterally cancel Brexit by reversing Article 50 – the day before the MPs’ crunch vote.
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The BBC understands Mrs May is exploring two different options to address the concerns of backbenchers.
The first option would see Parliament having a role in deciding whether to extend the transition period or enter the backstop arrangement, if no trade deal has been reached by the end of December 2020.
The transition period is due to kick-in when the UK leaves the EU on 29 March. It can only be extended once – but if the two sides have still not agreed a deal by the end of that second period, then the backstop will apply.
This would mean Northern Ireland staying aligned to some EU rules, which many MPs say is unacceptable. The UK would also not be able to leave the backstop arrangement without EU agreement.
The second option being explored with MPs, the BBC understands, is giving Parliament an annual vote on whether to stay in the backstop, once it has been activated, or to pursue other alternatives.
The BBC’s political editor Laura Kuennsberg said discussions were “very fluid” and no decision had been reached in government about which option to choose.
But the prime minister confirmed in her Today interview that giving MPs more control in this way is under discussion.
There are also talks on how this would be compatible with the government’s legal obligations under the EU withdrawal agreement, added our correspondent.
‘We have a choice’
Mrs May told BBC Radio 4’s Today programme she had not given up on winning the vote on her Brexit deal – negotiated over the past 18 months or so – despite dozens of her own MPs and all opposition parties being against it.
She said she recognised concerns about the Northern Ireland border backstop keeping the UK tied to the EU indefinitely.
And she conceded the UK would have “no unilateral right” to pull out of the backstop under her EU withdrawal agreement – but she said the UK would have a choice over whether or not to enter into it.
“The backstop is something nobody wants to go into in the first place, and we will be working to make sure that we don’t go into it,” she said.
“If we get to the point where it might be needed, we have a choice as to what we do, so we don’t even have to go into the backstop at that point.”
She suggested Parliament could be “given a role” in deciding whether to enter the backstop and how the UK would get out of it.
“I recognise there are concerns from colleagues about the role of Parliament, about the sovereignty of the UK in relation to that issue, so I am talking to colleagues about how we can look at Parliament having a role in going into that and, if you like, coming out of that,” she told Today.
She again ruled out a further referendum and rejected alternative Brexit plans suggested by different factions of her party.
“None of the other arrangements that people have put forward fully deliver on the referendum. This deal delivers on the referendum,” she said.
No confidence motion
The Commons debate on Thursday is focusing on the economic effects of Brexit.
Ministers are arguing it creates a unique partnership with the EU, while Labour insists it will make people poorer.
Meanwhile, Northern Ireland’s Democratic Unionist Party, which keeps Mrs May’s in power, has said it would support the government in a confidence motion if the deal was thrown out on Tuesday.
Sammy Wilson, the DUP’s Brexit spokesman, told Today: “Our grievance with the government has been that the government made a promise to us and to the people of Northern Ireland that Brexit would be delivered for the whole of the United Kingdom, and provided there is nothing introduced to break that promise, we have no reason to have no confidence in the government.”
But he added the DUP could still withdraw support for the government at a future date.