Labour leader Jeremy Corbyn has said he would be ready to back another EU referendum, if party members want one.
He said he would be "bound" by the outcome of a vote at the Labour Party conference - although he would prefer to have a general election.
But Unite leader Len McCluskey said any referendum should not include the option of remaining in the EU.
Meanwhile Brexit Secretary Dominic Raab ruled out a snap election this autumn, saying the idea was "for the birds".
The Labour Party has never formally rejected the option of a further vote, but both Mr Corbyn and his deputy, Tom Watson, have indicated they would prefer it to be resolved by a general election.
Pressed on the issue on BBC One's Andrew Marr Show, Mr Corbyn, who has said he is not calling for another referendum, said "our preference" is for a general election that would then allow a Labour government to negotiate the UK's future relationship with Europe.
He said: "Let's see what comes out of conference. Obviously I'm bound by the democracy of our party."
But he said it was "conjecture" to suggest any referendum backed at the conference would be on remaining or leaving the EU, adding: "We don't know what it would be."
Brexit is among the eight issues to have been chosen in a ballot by Labour members and trade unions for debate in Liverpool.
The others are Palestine, the economy, housing, schools, government contracts, in-work poverty and justice for the Windrush generation.
Discussions are to take place on Sunday evening to decide the final text of each motion.
BBC assistant political editor Norman Smith said much would depend on whether the Brexit motion clearly stated that Labour backed another referendum, or whether it would be more ambiguously worded so it did not tie the leadership's hands.
Mr Corbyn also told the programme the UK "could be" close to a general election. Amid speculation that Labour could force a vote of no confidence in Prime Minister Theresa May if Parliament rejects any Brexit deal, he said: "We will be putting our case to Parliament and we will see what happens after that. We are absolutely ready for it."
He said Labour would be prepared to vote down any deal Mrs May came back with, if it did not meet a series of tests Labour has set out.
The party has made several policy announcements ahead of its annual conference - which begins in Liverpool on Sunday - including:
- Plans to require businesses employing more than 250 people to reserve one-third of seats on boards for representatives of their workforce to help rein in a "reckless corporate culture"
- A proposed new tax for the owners of second homes in England, based on the value of the property, with the money raised being used to tackle homelessness
- Plans to make employers provide up to 10 days paid leave for victims of domestic violence
However, campaigners are using use the conference to pile pressure on the Labour leadership to support a further referendum.
Thousands of people marched through the centre of Liverpool, to a rally at the Pier Head, where the conference is taking place.
Protesters waved EU and other flags and chanted anti-Brexit slogans and "it's not a done deal" as they walked from St George's Hall. The event was organised by the cross-party People's Vote campaign for a referendum on the final Brexit deal.
Liverpool Wavertree MP Luciana Berger was among those who joined the march in support of Labour members who want the conference to debate supporting a second vote.
Some sections of the crowd chanted directly at Mr Corbyn, saying: "Hey Jeremy, take a note, for the many, People's Vote."
In a speech, Tottenham MP David Lammy asked: "Are you listening Jeremy Corbyn?"
Highlighting that people from across the UK were present, he said: "They are saying squarely to the leadership of the Labour Party: 'Listen to us, hear us, give us a People's Vote'.
"When we have that People's Vote, let us ensure that the option to remain in the EU is on the ballot paper."
But Unite leader Mr McCluskey told the BBC's Pienaar's Politics: "The referendum shouldn't be on 'do we want to go back into the European Union?'"
He added: "The people have already decided on that. We very rarely have referendums in this country. The people have decided against my wishes and my union's wishes but they've decided... For us to now enter some kind of campaign that opens up that issue again I think would be wrong."
According to a YouGov survey of 1,054 Labour members, commissioned by the People's Vote campaign, 86% wanted a final, public say on the outcome of Brexit negotiations, against 8% who opposed it.
But the Brexit supporting Labour MP Kate Hoey described calls for another vote as the "last gasp" of people who had never wanted to accept the result of the 2016 referendum.
She said another referendum was likely to be bigger than the last and, if a bigger majority voted to leave, "we're still in the same position".
On Saturday shadow chancellor John McDonnell warned people calling for another referendum to take into account the "real risk" of stoking racial tensions and far-right populism.
The UK is due to leave in March 2019 and Theresa May has been negotiating with other EU leaders on the UK's future relationship with the bloc.
In a statement on Sunday, the prime minister said "many in Labour, the Liberal Democrats and the SNP are trying to thwart Brexit at every step and seeking to exploit this moment for political gain" by calling for another referendum and extending Article 50 to delay Brexit.