Video report by ITV News Political Correspondent Daniel Hewitt
Mr Corbyn said that going “back to the people” was now the only option when faced with the prospect of a no-deal Brexit and an incoming Tory prime minister “with no mandate”.
The Labour leader has been under intense pressure to explicitly back a referendum on Brexit after the European elections saw his party suffer heavy losses.
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
Jeremy Corbyn has spoken in favour of a "public vote" on Brexit, saying that it is necessary to break the impasse in negotiations.
Speaking on a trip to Ireland today, Mr Corbyn said he did not support a "re-run" of the Brexit vote.
He said: "We don't back a re-run of 2016, that happened, that's gone.
"What I do say is if parliament comes to an agreement and its reasonable, then there should be a public vote on it, but that is some way off."
Labour has sought to appeal to both Leave voters in its northern seats and Remainers in London and other cities, but lost half its MEPs and took just a 14% vote share as support switched to the clear alternatives offered by the Brexit Party and pro-EU Lib Dems and Greens.
Mr Corbyn said the Tory leadership contest – and the prospect of a “no-deal zealot” becoming prime minister – meant the issue had to go to the public.
And in a sign that he would be prepared to work with Tory moderates to prevent a no-deal Brexit, possibly by tabling a confidence motion to bring down the Government, Mr Corbyn said he would do “whatever is necessary”.
He said: “Labour will work with anyone across party boundaries and do whatever is necessary to stop a disastrous no-deal outcome, which would open the way for a frenzy of deregulation and a race to the bottom in jobs, rights and protections.
“But 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.
“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.”
The Irish Times reported he told reporters in Dublin that a second referendum would not be a “re-run of 2016”, but “would be on a negotiated deal or alternatives to that”.
Asked if it would not be another “in-out” referendum, Mr Corbyn said: “It would be on the basis of whatever we have succeeded in negotiating.”
Labour MP Bridget Phillipson, who supports a referendum, said Mr Corbyn was “at last beginning to listen to what our voters and members are saying” but there is “no immediate prospect of a general election” so the party should throw its weight behind the People’s Vote campaign.
But Unite union boss Len McCluskey, who has warned against a second referendum, told ITV’s Peston: “My message to the Labour Party is don’t be spooked by these Euro elections.”
Meanwhile, deputy Labour leader Tom Watson said he would push for an all-member ballot to shift the party’s Brexit policy.
Mr Watson, a supporter of the campaign for another referendum, carried out a survey of party members to see how they wanted to proceed – a ballot, a special conference or delaying until Labour’s annual conference in September.
He said: “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.”
Meanwhile, Eurosceptic MP Jacob Rees-Mogg has said the European election results show that Britons have rejected “project fear”.
In an article for The Sun, the North East Somerset MP said: “In truth, the fears are like the supposed Millennium Bug, a fantasy of fevered minds.
“After all, with £39 billion, free-flowing trade and cheaper imports, as former Trade and Industry Secretary Peter Lilley has said: ‘It is not crashing out, it is cashing in’.”
Mr Corbyn’s comments on a public vote came ahead of meetings in Dublin with Taoiseach Leo Varadkar and President Michael D Higgins.
The Labour leader warned the Tory leadership contest would damage communities on both sides of the Brexit divide in Britain.
“Throughout this summer, our politics will be paralysed and our country’s future put on hold while the Conservatives are locked in internal conflict over their leadership,” he said.
“Jobs and investment will be put at risk in Leave and Remain areas alike.
“The Tory leadership contest will most likely end with a small number of wildly unrepresentative right wing Conservative activists foisting a no deal zealot on the country.
“The next Tory leader will be yet another unelected prime minister, without the support of the public and with no mandate for whatever form of Brexit he or she supports.
“Since the 2016 referendum, Labour has backed an alternative plan for Brexit that would work for the whole country, protecting jobs and living standards.
“Brexit has not happened because of the sheer incompetence and infighting of the Conservative Party.”