Labour has said it is prepared to back another EU referendum to prevent a "damaging Tory Brexit".
The party's leader, Jeremy Corbyn, is to tell Labour MPs later that the party will move to back another vote if their own proposed Brexit deal is rejected on Wednesday.
The BBC's Vicky Young said it was a highly "significant" development as Mr Corbyn has previously been "lukewarm" about the idea of another vote.
UK Prime Minister Theresa May is under growing pressure to delay the 29 March Brexit date.
Labour is not yet making clear what its proposed referendum would be on.
When asked to clarify this, a spokesman for the leader's office said: "We've just said we'd back a public vote to prevent a damaging Tory Brexit."
But the prime minister, who will update MPs on the latest negotiations on Tuesday, has insisted the UK can still leave next month as planned.
Mr Corbyn will tell his MPs later that Mrs May is "recklessly running down the clock" in an attempt to "force MPs to choose between her botched deal and a disastrous no deal".
"We cannot and will not accept," he will say.
He will say Labour will also put down an amendment this week setting out its plan for a "comprehensive customs union" and "close alignment" with the single market.
The amendment also sets out guarantees on rights and standards, protection for Britain's role in EU agencies and a security agreement which guarantees access to the European arrest warrant and "vital" shared databases, he will say.
Ahead of a series of votes on Brexit on Wednesday, Labour has also said the party will support a cross-party amendment, proposed by Labour's Yvette Cooper and Tory MP Sir Oliver Letwin, designed to rule out the prospect of a no-deal exit.
Mr Corbyn will say: "One way or another, we will do everything in our power to prevent no deal and oppose a damaging Tory Brexit based on Theresa May's overwhelmingly rejected deal.
"That's why, in line with our conference policy, we are committed to also putting forward or supporting an amendment in favour of a public vote to prevent a damaging Tory Brexit being forced on the country."
At their conference last autumn, Labour members backed a policy of keeping all options on the table, including holding another referendum, if it could not force a general election.
However, many Labour MPs believe the party has been slowly distancing itself from that commitment after it failed to win a vote of no confidence against the government last month.
Nine Labour MPs have quit the party in the past week, partly in protest at its stance on Brexit.
Shadow Brexit Secretary Sir Keir Starmer insisted the party would "deliver" on its promises.
Labour MP David Lammy, who backs a "People's Vote" on the terms of the UK's exit, welcomed the move by his party to "back the principle" of a referendum.
"Even if MPs can agree some sort of deal, it would be wrong to force it on the British people when we now know so many of the promises made in 2016 have been broken, and any deal will be worse than the one we've already got inside the EU," he said.
Labour's Hilary Benn, who chairs the Commons Brexit committee, said talk of a referendum was still some way off as MPs would have another opportunity to vote on Theresa May's deal by 12 March.
But if the deal was rejected, he said, it would "open up" a range of other possibilities, one of which would be to put the final decision "in the people's hands".
Liberal Democrats leader Vince Cable said he welcomed the news.
"My party will work with Labour and others to secure a People's Vote with an option to remain," he said.
"We have long argued it is the right and logical thing to do for the people to have the final say on Brexit."
Labour's position on Brexit
- June 2017 - Labour's general election manifesto accepts referendum result
- March 2018 - Shadow Northern Ireland secretary Owen Smith sacked for supporting second referendum on final deal
- September - Labour agrees if a general election cannot be achieved it "must support all options … including a public vote"
- 28 November - Shadow Chancellor John McDonnell says Labour will "inevitably" back a second referendum if unable to secure general election
- 16 January 2019 - 71 Labour MPs say they support a public vote
- 21 January - Shadow International Trade Secretary Barry Gardiner says if a second referendum motion was put to MPs, Labour would support it
- 6 February - Mr Corbyn writes a letter to Mrs May outlining five changes with no mention of a "People's Vote"
- 25 February - Labour says it will back a public vote if its proposed Brexit deal is rejected on Wednesday