Jeremy Corbyn has refused to follow two senior colleagues who say they would back Remain in any further Brexit referendum.
His close allies Diane Abbott and John McDonnell both say they would campaign for Remain, regardless of the other options on the ballot paper.
But the Labour leader chose only to say he would campaign for Remain if the alternative was no deal.
Earlier, Ms Abbott said Mr Corbyn would “follow what the party says”.
The Labour leader has been under pressure for months to give his full-throated support to continued EU membership.
More and more of his senior colleagues have come round to that position, some blaming lacklustre election results for the party earlier this year on its Brexit equivocation.
Speaking on Tuesday, Mr Corbyn was asked whether he too would campaign for Remain, even against an alternative Brexit deal negotiated by any future Labour government.
He replied: “What we’ve said is, if it’s no deal or Remain, we’ll campaign for Remain.”
Pressed for further clarification, he repeated: “Between no deal and remain, I’ll argue for remain.”
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Mr Corbyn has outlined a plan to stop a no-deal Brexit, which involves defeating the government in a no-confidence vote then becoming a caretaker PM.
If he succeeds, he hopes to head a temporary government which would delay the Brexit date and hold a general election.
In that general election, Labour would call for a “public vote” – a referendum – on the terms of leaving the European Union.
In the public vote he has said he wants “credible options for both sides”, including the option to remain.
It is not yet clear whether any Labour government would try to reopen negotiations with the EU over a deal to leave, or proceed straight to a referendum.
The party has told the BBC it would decide this when it produced its manifesto, which it will need to publish if a general election is called.
Lib Dem leader Jo Swinson tweeted that Mr Corbyn would not “fight for Remain”.
“He wants to deliver a Labour Brexit, because he is a Brexiteer,” she said.
Earlier, shadow home secretary Diane Abbott confirmed she would “personally” campaign for Remain in the event another referendum is held.
She told BBC Radio 4’s Today programme remaining would be the “best option for the country and my constituents”.
“The party and the shadow cabinet will have to debate this and arrive at a position – whatever the position is Jeremy will follow what the party says.”
On Monday, shadow chancellor John McDonnell made the same commitment, adding he couldn’t envisage another option with the “same benefits as Remain”.
Asked whether the party could even stay neutral in a referendum, he replied: “That’s one of the issues we’ve got to debate in the party.”
“I know people get frustrated with this […] but we’re a democratic party,” he added.
“If you sign up to democratic rules, you have to abide by them.”
Not an easy choice
Mr Corbyn’s “credible leave option” would presumably resemble Labour’s previous policy of maintaining a close relationship with Brussels.
But Diane Abbott also suggested her leader would “follow what the party says” – so at this year’s annual conference there will be a concerted push to get the party to commit to Remain
But some powerful voices – including the leadership of the giant Unite union – are still likely to resist.
Labour insiders expect an early election. Remainers – including Ms Abbott – fear an equivocal policy will gift votes to the Lib Dems.
Labour Leavers say an all-out Remain position will gift votes to the Brexit Party.
Not an easy choice.
But with more of Jeremy Corbyn’s usual allies – including John McDonnell – now backing Remain, it feels that this option is gaining momentum.
Jeremy Corbyn refuses to echo allies’ Brexit position}