- Video report by ITV News Political Correspondent Paul Brand
Mr Watson had given a speech calling for a second EU referendum to be held first, before the party moves for an election, claiming a national poll may not break the Brexit deadlock.
His latest intervention puts him on a fresh collision course with his boss - Mr Corbyn - who hours later openly disagreed with Mr Watson, further widening the Brexit divide between the pair.
He said his priority was to "prevent a no-deal exit from the European Union, that is our first priority - after that, we want a general election".
Pressed on whether Mr Watson was wrong to say Labour should be going for a referendum first, the Labour leader said: "It's Tom's view - I don't accept it, I don't agree with it."
Earlier in the day Labour's shadow Brexit secretary Sir Keir Starmer claimed Labour is "united around the idea there should be a referendum" on the outcome of Brexit.
He did however say the party having "good discussions" around a second referendum, adding, "we are not shutting down the discussion unlike Johnson and Cummings".
On his way to give a speech to the Trade Union Congress (TUC), he said: "We should have a referendum in our manifesto and that remain should be one of the options".
"We're united around the idea there should be a referendum on any outcome this government puts forward."
While Sir Keir didn't contradict Labour Party policy in saying he wants a referendum, Mr Watson did.
That puts him on a collision course with Labour leader Jeremy Corbyn, who has made clear his priority is for an election once Parliament has closed off a no-deal Brexit.
In a speech on Wednesday in London, Mr Watson said a single-issue Brexit election may not break the deadlock in Parliament - something only a second referendum can achieve with certainty.
He argued that if a referendum were to follow an election, then Labour should commit "unambiguously and unequivocally" to campaign for Remain.
Again, his view sets him up for a clash with Mr Corbyn who is yet to say which side he would support, and has said that Labour must appeal to both Leave and Remain supporters.
He defended himself against a suggestion he was muddying the waters by publicly discussing a position running counter to that of his party.
Labour's deputy leader told the Creative Industries Federation in London: "It does seem to me that compromise is in the air."
He cited Conservative MPs who have moved towards favouring a second referendum and Labour figures wanting a deal, and 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 speech was a pitch for Jeremy Corbyn's job.
"It isn't a job application that I gave today and nor is it a resignation," he said.
Mr Corbyn's ambiguity is thought to be due to the fact that many Labour supporters backed both sides in the June 2016 referendum, and he does not want to take a firm stance and alienate one side.
The 70-year-old said an incoming Labour government would hold a new referendum - with Remain and a "credible" option for Leave on the ballot paper.