Jeremy Corbyn has said a second referendum is “some way off” and that Labour still wants to negotiate a better Brexit deal, resisting pressure from shadow cabinet ministers to commit to campaigning immediately for a public vote.

Speaking in Dublin, the Labour leader said the only way to break the deadlock would be a general election or a second referendum after negotiating a softer Brexit deal with Brussels.

Corbyn said there must not be a repeat of the 2016 referendum on Britain’s EU membership, and argued that Labour could strike a better agreement with Brussels that would include a customs union, which would then be put to a public vote.

He said: “We don’t back a rerun of 2016. That happened. That is gone. What I do say is that if parliament comes to an agreement, then it’s reasonable, and if parliament wishes it, there should be a public vote on it but that is some way off.”

Speaking to reporters before meetings with Irish politicians and trade unions, Corbyn said Labour would still like a deal negotiated with the EU that includes a customs union and greater protections for workers rights and environmental standards.

Facebook Twitter Pinterest Jeremy Corbyn and the taoiseach, Leo Varadkar, on Thursday. Photograph: MerrionStreet/PA

He also said that the choice in a referendum would be about whatever deal was negotiated, with Labour later confirming that remain would be on the ballot under any circumstances.

Corbyn said: “I would go back to the EU, explain that we had fought an election campaign in order to make sure there was a good relationship with Europe in the future, that we weren’t afraid of public opinion on this, and ask them to seriously consider what we are suggesting, which is a customs union with a British say and trade relationship with Europe, and a dynamic relationship on rights would not be undermining Europe on workers rights, on consumer rights, on environmental protections.”

Corbyns’s remarks leave open the option of Labour campaigning in favour of a Brexit deal in any second referendum, rather than for the option of remaining in the EU, which is favoured by many shadow cabinet ministers.

Corbyn still backs soft Brexit and rejects in/out referendum – live news Read more

He also said he would do whatever was necessary to stop a no-deal Brexit, which could include working with Conservative moderates to bring the government down.

“Faced with the threat of no deal and a prime minister with no mandate, the only way out of the Brexit crisis ripping our country apart is now to go back to the people,” he said. “Let the people decide the country’s future, either in a general election or through a public vote on any deal agreed by parliament. For Labour any outcome has to work for our whole country, not just one side of this deliberately inflamed divide.”

Labour’s preference is still for a general election but Corbyn’s tone on a second referendum shifted earlier this week to say he would back a poll on any deal. The move came after Labour fell to third place in the European elections on just 14% of the vote, losing ground to both the Liberal Democrats and the Greens.

In contrast, Tom Watson, Labour’s deputy leader, is campaigning for Labour to get fully behind a second referendum. He released the results of a survey suggesting that the vast majority of Labour members who replied wanted an all-member ballot to decide on whether to change the party’s Brexit policy.

“The results of my Brexit poll are clear: 84% of Labour members and supporters who took the survey want an all-member ballot to decide our party’s Brexit policy. As deputy leader I’ll support them to make this happen,” he said.

In response to Corbyn’s interview, the Labour MP Wes Streeting, who is campaigning for a “people’s vote”, said: “It’s time for Jeremy Corbyn to stop wriggling and start leading. The overwhelming majority of Labour members and Labour voters now know that giving the public the final say on Brexit is the only way to deliver a lasting and stable conclusion to this crisis.

“If the simple fact that continued ambiguity on Brexit is badly damaging our party wasn’t clear enough already, the disastrous results of the European elections for Labour should have rammed it home. Our vote share sunk to historic lows, it was arguably the worst ever election result for the Labour party in its modern form. And by a margin of more than four to one Labour voters were flocking to parties that give unequivocal backing for a final-say referendum rather than Nigel Farage’s party.”

On the other side of the debate, the shadow cabinet ministers Ian Lavery and Jon Trickett have opposed a second referendum, along with Len McCluskey, the general secretary of Unite. McCluskey told ITV’s Peston: “My message to the Labour party is don’t be spooked by these Euro elections.”