He urged the Labour leader to “get off the fence” and support such a ballot.
His comments comes as Labour candidates in the European elections have put further pressure on the party to back a second referendum.
A group of 22 candidates, including the leader of Labour’s MEPs Richard Corbett and 11 others seeking to retain their seats in the European Parliament, have pledged to campaign for a public vote and to support remaining in the EU.
The move comes ahead of a crunch meeting of Labour’s National Executive Committee on Tuesday that will decide the manifesto for the May 23 contest.
The pledge was organised by the Remain Labour group, whose founder Andrew Lewin said:
“The overwhelming majority of Labour members and voters want to Remain in the EU and I am delighted that so many of our candidates have pledged to campaign for that outcome in the European elections.
“I hope and expect that more will join them in the coming days.
“Remain voters across the country who want to defeat Nigel Farage’s Brexit Party can now vote with confidence and enthusiasm for Labour candidates who have pledged to fight for our future, as members of the European Union.”
Sitting MEPs who have signed the pledge are: Alex Mayer (East of England), Seb Dance (London), Jude Kirton-Darling (North East), Paul Brannen (North East), Theresa Griffin (North West), Julie Ward (North West), Wajid Khan (North West), David Martin (Scotland), John Howarth (South East), Clare Moody (South West), Sion Simon (West Midlands) and Mr Corbett (Yorkshire and the Humber).
A further 10 MEP candidates back the move: Anna Smith (East of England), James Beckles (London), Amy Fowler (South East), Rohit Dasgupta (South East), Duncan Enright (South East), Lord Adonis (South West), Jackie Jones (Wales), Matthew Dorrance (Wales), Mary Wimbury (Wales) and Mark Whitcutt (Wales).
In a separate development aimed at putting pressure on Mr Corbyn’s party to fully throw its weight behind another referendum, the People’s Vote campaign launched an online tool to allow voters to find out where candidates stand on the issue.
The peoplesvotetest.uk website allows members of the public to check which parties in their area support a new vote on Brexit and includes a “register to vote” feature ahead of the deadline for registration on May 7.
James McGrory, executive director of the People’s Vote campaign, said: “Voters need to know which parties are listening to the growing calls for Brexit to be put back to the people. And, whichever party you choose to support, you need to register to vote if you want your voice heard.
“That’s especially important for young people, who overwhelmingly support a People’s Vote but who are less likely to be on the electoral register.
“The People’s Vote campaign is cross-party, our supporters and activists come from all parties and none, and we’re very proud of that.
“This new website will allow the public to see all the information about which parties have committed to giving the people the final say on Brexit and to decide for themselves who they want to vote for in the European elections.”