A Labour source said: 'Our MEPs are all pro-Brussels and do not want to fight alongside anti-Brussels Labour candidates because they say it will show the leadership is facing both ways.
The row was revealed after Richard Corbett, Labour's leader in the European parliament, said Mr Corbyn must back a second referendum - or "confirmatory vote" - in its Euro elections manifesto.
"It was on the 29th when we didn't leave; that's when this has all gone wrong".
He said that a referendum has been voted on and defeated in recent House of Commons votes.
A total of 17 Labour MEPs have publicly supported the People's Vote - even though most represent Leave-supporting constituencies.
She has been unable to persuade MPs to back the withdrawal terms she has struck with Brussels, but is also unwilling to take Britain out of the European Union with no deal at all.
Despite being handed an extension of EU membership until October 31, May is hoping to pass a withdrawal agreement and lead Britain out of the bloc before May 23 to avoid taking part in elections for the European Parliament.
He told Sky News: 'I really urge the Prime Minister to be very clear that we are not fighting the European elections.
He said there was "no date ringed in the calendar" for the talks to end but if agreement could not be reached on some form of Brexit deal, then he hoped the two sides would be able to agree a binding mechanism for parliament to agree a way forward.
The Conservatives are set to lose out in local elections due on May 2nd, with one polling expert, Lord Hayward, saying the party faced a "Brexit penalty".
Energy minister Claire Perry yesterday said it was still possible that the elections could be cancelled if Parliament passed a Brexit deal after MPs return from their Easter break.
The British government will resume talks with the main opposition Labour party next week on how to resolve the deadlock over Brexit, a senior minister said Sunday.
The MP for Chingford and Woodford Green warned against his party embracing Labour's Brexit policy, saying he had "real concerns with some of my colleagues going out lauding Jeremy Corbyn".
He added: "I am a little bit anxious that the European Union in future will be determining trade deals and we won't really have a say".
Duncan Smith has now requested that she stands down in May and described talks with Labour as a "recipe for disaster".