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 a backstop.
Meanwhile No 10 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 has said it will deliver a ruling on Monday on whether the UK could unilaterally cancel Brexit by reversing Article 50 – the day before the MPs’ crunch vote.
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.
She conceded that 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 told Today.
The BBC’s Political Editor Laura Kuenssberg said she was not convinced Mrs May’s words on the backstop would “peel away many rebels” and they would also cause concern in the EU because the backstop was part of a “legal text” agreed with the prime minister.
Brexit’s economic effects will be the focus of a Commons debate later.
Ministers will say it creates a unique partnership with the EU, while Labour argues it will make people poorer.
The Daily Telegraph reported that the EU could be prepared to discuss extending Article 50 – delaying Brexit until after 29 March – if the deal was rejected by MPs.
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.
The backstop is designed to protect the Northern Ireland peace process by preventing the return of customs posts and checkpoints at the Irish border, in the event a future UK-EU trade deal was not agreed.
However, while it would keep the entire UK temporarily under EU customs rules, it would require some new checks on goods transported to Northern Ireland from Great Britain, which the DUP says is unacceptable.
The full legal advice presented to cabinet before the Brexit deal was agreed was published on Wednesday, after the government lost a bid to keep it confidential.
It revealed the chief law officer’s opinion that the backstop risked a “protracted rounds of negotiations” with the EU, could potentially last “indefinitely”, and that the UK could not “lawfully exit” without EU agreement.
The DUP said this would be “devastating” for the UK.
Sammy Wilson, the DUP’s Brexit spokesman, told BBC Radio 4’s Today programme: “We would certainly not vote to topple the government because we would have no reason to do so.
“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.”
However, he said the DUP could still withdraw support for the government at a future date.
Parliament could ‘steal Brexit’
Thursday’s debate will be opened at 11:30 GMT by Chancellor Philip Hammond, with International Trade Secretary Liam Fox expected to round off proceedings after about eight hours.
On Wednesday, Mr Hammond told the Commons Treasury committee: “When there is a deal on the table that has very, very modest costs to the economy, which will allow us to move on as a nation both economically and politically, I judge that even narrowly, economically that will be in the best interests of the country.”
Mr Fox has warned of a risk of Parliament trying to “steal Brexit from the British people”, after MPs voted to give themselves a greater say over the process.
He said there was a “natural Remain majority” in Parliament and that any attempts to delay the UK’s departure or overturn the 2016 referendum result would be a “democratic affront”.