Following mounting pressure on the Labour leader to back a public vote after the party suffered heavy losses in last week’s EU elections, Mr Corbyn has seemingly relented to Remain campaigners.
He 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”.
However, he stopped short of saying a second vote would be between Leave and Remain - hinting that it could be on a deal versus no-deal.
Divisions within Labour were further exposed by the decision to expel Alastair Campbell, one of the architects of New Labour, for voting for the Liberal Democrats in protest at his own party's Brexit policy.
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.
‘Not a re-run of 2016’
The Irish Times reported Mr Corbyn 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.
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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.”
However, Labour’s chairman Ian Lavery opened up Labour splits by describing those calling for a second referendum as “sneering left-wing intellectuals”.
He wrote in the Guardian: “As someone who has opposed a so-called public vote, not least because parliament has no majority for it in principle and nobody has the faintest idea what we would actually put on the ballot, I have been doggedly attacked by certain sections of the party, as well as those on the outside.
“It does feel that a certain portion of ‘left-wing intellectuals’ are sneering at ordinary people and piling on those trying to convey the feelings of hundreds of thousands of Labour voters.”
He added: “We cannot win a general election by simply fighting for the biggest share of the 48%.”
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.”
‘No more project fear’
Eurosceptic MP Jacob Rees-Mogg 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’."