A motion of no confidence in Jeremy Corbyn's leadership of the Labour Party has been tabled for next week amid criticism of his handling of the EU referendum campaign.
However Mr Corbyn said he was "absolutely staying", pledging to continue to campaign against austerity, for "decent" services and a good relationship with Europe.
Labour MPs Margaret Hodge and Ann Coffey called for a debate on his performance as leader in a letter to the chair of the Parliamentary Labour Party (PLP).
"We wish to submit a motion for urgent consideration by the Parliamentary Labour Party as follows: that this PLP has no confidence in Jeremy Corbyn as Leader of the Parliamentary Labour Party," they wrote.
"Given the importance of this issue, I would urge you to bring forward consideration of this motion for discussion on Monday ... with a ballot of colleagues on Tuesday."
Mr Corbyn has come under fire for failing to persuade Labour voters to back the Remain campaign.
Former Shadow Chancellor Chris Leslie told BBC News: "I would say today he does need to consider his position and think about whether he should do the honourable thing.
"Every MP is going to have to search their conscience about it but I think I would need an awful lot of persuading to have confidence in Jeremy's leadership going into a general election."
Labour MP Angela Smith also called for Mr Corbyn to "consider his position", saying he had showed "insufficient leadership" over the issue.
And another leading backbencher told The Independent that there had been "a failure of Labour leadership", claiming that a better campaign by the party could have swayed half a million voters.
A no-confidence motion does not have any formal power that would force Mr Corbyn to resign, but it would significantly increase pressure on him.
And the chair of the PLP, left-wing MP John Cryer, could decide that the motion should not be debated. If he allows the vote, MPs would do so by secret ballot.
In an interview with ITV News, Mr Corbyn said: "Absolutely I'm staying [as Labour leader], absolutely I'll be campaigning for social justice in this country, absolutely opposing any austerity budget, absolutely campaigning for decent health services, decent housing and job protection in this country, and a good relationship with Europe in the future."
