Remain supporters have criticised Jeremy Corbyn for saying he would continue to pursue Brexit if his party won a snap general election in 2019.
Speaking to the Guardian, the Labour leader said he would go to Brussels to negotiate a better deal than the one Theresa May has offered to Parliament.
Asked what stance Labour would take if another referendum took place, he said it would be for the party to decide.
Labour's Chuka Umunna said the interview was "deeply depressing".
Mr Corbyn also admitted he was "extremely angry" during Prime Minister's Questions on Wednesday, but has denied calling Theresa May a "stupid woman".
The Labour leader has repeatedly called for a general election to solve the deadlock in the Commons over the prime minister's Brexit deal, which many MPs on all sides of the House have vowed to vote down.
He told the paper the earliest an election could take place is February - as a month needs to pass after a government has resigned before a vote can take place.
But if Labour won, he said he would still want to pursue Brexit, and try to get a deal agreed before 29 March 2019 - the day the UK is set to leave the EU.
"You'd have to go back, and negotiate, and see what the timetable would be," he said.
'A matter for the party'
A number of Mr Corbyn's own MPs back a "People's Vote" to ask the public their opinion of the deal.
But asked if he could see such a referendum taking place, he offered no support, saying: "I think we should vote down this deal; we should then go back to the EU with a discussion about a customs union."
When questioned over the stance Labour would take were a referendum to take place, he said: "It would be a matter for the party to decide what the policy would be.
"But my proposal at this moment is that we go forward, trying to get a customs union with the EU, in which we would be able to be proper trading partners."
Writing on Facebook, former minister Mr Umunna - a leading member of the cross-party People's Vote for a second EU referendum - said his leader's comments were "disappointing".
He wrote: "Brexit is essentially a project of the hard right of British politics who want to turn Britain into a lightly regulated, offshore tax haven for the super rich, devoid of proper protections for workers, and one which seeks to dump the blame for the UK's problems on immigrants.
"Labour should stop pretending there is a 'good' Brexit deal and we should certainly not be sponsoring this project because Brexit is the problem - it solves nothing."
Fellow Labour MP Wes Streeting also criticised Mr Corbyn's remarks, saying: "Why peddle this myth that Labour would be able to renegotiate a Brexit deal at this 11th hour? How would Labour's Brexit be any better than remaining in the EU?
"Our members and voters are overwhelmingly pro-European. This lets them, and our country, down."
And Luciana Berger said her party would never be forgiven if it facilitated Brexit.
Rival parties, who want to remain in the EU, also attacked Mr Corbyn's comments, with the SNP's Westminster leader Ian Blackford calling the Labour leader "the midwife to the delivery of the Tory's Brexit plans".
Lib Dem leader Vince Cable said Mr Corbyn "refuses once again to take the blinkers off", adding: "On Brexit, you simply cannot put a cigarette paper between Theresa May and Jeremy Corbyn."
And Caroline Lucas of the Green Party said it made the case for a People's Vote even stronger if this was the direction Labour would take.