Mr Watson wrote in the Observer that the Labour Party is likely to lose to the Brexit Party in the European elections if voters believe that “we half agree with him”.
The Labour MP warned that his party could not “sit on the fence” on such a big issue as Brexit.
He said it was important that the Labour Party expresses how its government would be able to advance socialist values by working with other parties inside the EU.
He wrote: “We cannot just sit back, watch this fight on the far right, and allow Farage to prosper with a backward-looking brand of politics that offers no solutions.
“Instead we must offer a radical alternative based on our values that speaks directly to the people we represent and demonstrate Labour has a way forward out of the crisis.
“Labour won’t defeat Farage by being mealy-mouthed and sounding as if we half agree with him.
“We won’t beat him unless we can inspire the millions crying out for a different direction.
“We won’t win if we sit on the fence about the most crucial issue facing our country for a generation.”
However, former Ukip leader Nigel Farage has spoken out against a new referendum calling it a “total insult” to the 2016 Leave voters.
The Labour Party has said that its priority is to achieve the best Brexit deal for jobs and living standards so they can improve the economy and invest in all communities.
Mr Farage’s Brexit Party has signed up 60,000 paying supporters in only nine days and it hopes to have even more members than the Conservatives by the time of the EU elections in May.
In a tweet Mr Watson also said: “Labour won’t defeat Nigel Farage by being mealy-mouthed and sounding as if we half agree with him.
“We won’t win if we sit on the fence about the most crucial issue that has faced our country for many generations.”