Theresa May has said the Commons vote on her Brexit deal will “definitely” go ahead next week.
She told the BBC she was seeking assurances from the EU to address the concerns of MPs, as well as specific measures relating to Northern Ireland.
She also said she would look at giving Parliament a greater say in how the UK’s future relationship is negotiated.
But a poll carried out for the People’s Vote campaign suggests fewer than one in four voters support her Brexit deal.
MPs are due to vote on whether to back Mrs May’s Brexit plan in the next two weeks.
Asked by the BBC’s Andrew Marr if the vote – which was postponed last month – would go ahead, she replied “definitely”.
She said the UK would be in “unchartered territory” if the Commons rejected the terms of the UK’s withdrawal but asked repeatedly if she would seek further votes if this happened, she declined to say.
The UK is due to leave the EU on 29 March 2019 – regardless of whether there is a deal with the EU or not.
A deal on the terms of the UK’s divorce and the framework of future relations has been agreed between the prime minister and the EU – but it needs to pass a vote by MPs in Parliament before it is accepted.
The House of Commons vote had been scheduled to take place in December but Mrs May called it off after it became clear that not enough MPs would vote for her deal.
The debate on the deal will restart on Wednesday, with the crucial vote now expected to take place on 15 January.
Writing in the Mail, Mrs May said: “The only way to both honour the result of the referendum and protect jobs and security is by backing the deal that is on the table.”
She said “no one else has an alternative plan” that delivers on the EU referendum result, protects jobs and provides certainty to businesses.
“There are some in Parliament who, despite voting in favour of holding the referendum, voting in favour of triggering Article 50 and standing on manifestos committed to delivering Brexit, now want to stop us leaving by holding another referendum,” she said.
“Others across the House of Commons are so focused on their particular vision of Brexit that they risk making a perfect ideal the enemy of a good deal.
“Both groups are motivated by what they think is best for the country, but both must realise the risks they are running with our democracy and the livelihoods of our constituents.”