In comments that could reignite Labour’s debate over its Brexit policy, the party’s deputy leader said that, while an election might seem “inevitable”, campaigns where single issues dominate the agenda were never desirable.
Mr Watson said: “Boris Johnson has already conceded that the Brexit crisis can only be solved by the British people.
“But the only way to break the Brexit deadlock once and for all is a public vote in a referendum.
“A general election might well fail to solve this Brexit chaos.”
Jeremy Corbyn dismissed the suggestion, saying his priority is for an election once a no-deal Brexit on 31 October has been avoided.
Speaking at the TUC conference in Brighton on Tuesday, he said an incoming Labour government would hold a second referendum.
Mr Corbyn said remaining in the EU and a “credible” option to leave the bloc would be on the ballot paper.
But he has yet to say which of these he would support.
The Labour leader later delivered a firmer opposition to his deputy.
“It’s Tom’s view, I don’t acept it and I don’t agree with it,” he said.
Mr Watson firmly nailed his colours to the mast in his speech, saying that his party should commit “unambiguously and unequivocally” to campaigning for Remain.
And he argued it was not too late for Labour to win back Remain voters who may have been off by the party’s perceived confusion over its Brexit position.
Mr Watson told the Creative Industries Federation in London: “My experience on the doorstep tells me most of those who’ve deserted us over our Brexit policy did so with deep regret and would greatly prefer to come back; they just want us to take an unequivocal position that whatever happens we’ll fight to Remain, and to sound like we mean it.
“If we did it we could win, whereas if we don’t I fear we won’t.”
Mr Watson has clashed with Mr Corbyn in the past on the issue of a second referendum, as well as the party’s handling of antisemitism complaints.
He defended himself against the suggestion that he was being unhelpful by publicly discussing a position that was not party policy.
The MP added: “Everyone knows we have got to give a little to find a parliamentary solution to what is a national crisis.
“All I’m saying, to do with my own personal contribution, let’s all give a little and maybe we can find a way through this.”
He also denied his intervention was a pitch for Mr Corbyn’s job, saying: “It isn’t a job application that I gave today and nor is it a resignation.”
Meanwhile, Mr Watson’s shadow cabinet colleague Sir Keir Starmer has insisted that Labour will not be silenced in its attempts to stop a no-deal Brexit following Boris Johnson’s suspension of parliament.
In a speech to the TUC, the shadow Brexit secretary said: “Prime Minister Johnson now thinks that by shutting down parliament he will shut us up. Nothing could be further from the truth.
“Just as we worked throughout the summer to pass a law preventing no-deal, so we will work each and every day we are shut down to enforce that law.”
Sir Keir echoed Mr Watson’s call for a second referendum, saying it was the “only way” to break the deadlock and “clean up the mess left by the Tories”.
He added: “And that is why Jeremy was right to say at Congress yesterday that an incoming Labour government will commit to a referendum.”
Responding to Mr Watson’s remarks, Conservative Party chairman James Cleverly said they showed Labour wanted to overturn the 2016 referendum result.
He added: “This latest trick would mean delaying Brexit again for up to a year, handing over £250m a week to Brussels for no purpose.
“Labour are running scared of an election and only offer more dither and pointless delay.
“Only Boris Johnson and the Conservatives will deliver Brexit by 31 October, no ifs or buts, so we can move on and focus on the issues that matter to people – investing in the NHS, reducing violent crime and cutting the cost of living.”