Jeremy Corbyn has challenged the next Tory leader to hold another referendum before taking Britain out of the EU, saying Labour will campaign for Remain.
Mr Corbyn says the party will take this position to stop “no deal or a damaging Tory Brexit”.
But he does not say what he would do if he won a general election and was placed in charge of the Brexit process.
Some senior members of his team want him to take a pro-Remain stance in any circumstances.
In a letter to members, Mr Corbyn said: “Whoever becomes the new prime minister should have the confidence to put their deal, or no deal, back to the people in a public vote.
“In those circumstances, I want to make it clear that Labour would campaign for Remain against either no deal or a Tory deal that does not protect the economy and jobs.”
The announcement follows a shadow cabinet meeting on Tuesday morning, and a meeting with trade union leaders on Monday.
Labour’s Hilary Benn – who chairs the Brexit select committee – said it was a “big step forward” and called it “significant”.
He added: “We can now see there is nothing that can be better negotiated that is better for jobs, that is better than the deal we currently have.”
The bosses of Labour’s five-biggest affiliated unions called for the move the party has made – but also for it to hold a “confirmatory vote” on any new deal it negotiated if Labour won a general election.
The BBC’s political correspondent Iain Watson said there was disagreement about the second part of the unions’ stance in the shadow cabinet meeting, with deputy leader Tom Watson wanting a “straight Remain stance”, meaning a decision on it was “kicked down the road”.
Mr Watson is among other leading figures who have called for an unambiguously pro-Remain stance amid criticism that confusion over Labour’s message contributed to its poor performance in the recent European Parliament elections.
But MPs from Leave areas of the UK have warned it could damage the party’s next election performance.
In his letter, Mr Corbyn said Labour continued to believe the “compromise plan” set out for Brexit during cross-party talks with the government earlier this year was still a “sensible alternative that could bring the country together”.
This included a customs union, a strong single market relationship and the protection of environmental regulations and rights at work.
He renewed calls for a general election in the letter, saying Labour had a “crucial, historic duty to safeguard jobs, rights and living standards, but no Brexit outcome alone can do that.”
But Mr Corbyn did not say if Labour would pursue a new deal or a further referendum if the party won a general election – or stick to its manifesto commitment to accept the 2016 result.
Shadow Treasury minister Clive Lewis said if a snap election was called, Labour would try to renegotiate the Brexit deal agreed by Theresa May, despite saying it “very much looks like” Labour is now the party of Remain.
He told the BBC’s Politics Live: “If we win that general election, we will come into power, and if we can renegotiate that deal – a Labour deal – we will because that’s what people asked for.”
But asked if he would campaign for his own party’s deal in a referendum, he said: “No, I wouldn’t.”