Labour could abstain when the Withdrawal Agreement Bill comes before the House of Commons next month.
A spokesman for Jeremy Corbyn said that the Labour Party would not be able to support the bill when MPs are expected to vote on it at the start of June, but refused to rule out six times the party abstaining on the matter.
Abstention of the bill would fail to give Theresa May’s Brexit deal enough opposition to stop it from passing.
The spokesman said: “We voted to trigger Article 50, we respect the result of the referendum.”
They added: “We’re not in the business of getting into a car without knowing where it’s going.”
It would be unusual for the opposition to abstain on a major piece of legislation, but following local elections the Labour leader had claimed there was now a “huge impetus” to deliver Brexit.
The refusal to rule it out has alarmed a number of anti-Brexit campaigners.
However, political commentators are split on whether the party would go through with it.
HuffPost’s Paul Waugh tweeted: “I may be in a minority, but my own takeaway from post-PMQs briefing by Corbyn spokesman is that Labour will *not* abstain on the Withdrawal Agreement Bill 2nd reading.”
LBC’s Theo Usherwood said: “I cannot see Corbyn whipping his MPs to abstain.”
He added that if the bill fails it would give Labour the best chance of a general election.
The Sun’s Tom Newton Dunn, however, said it was “very significant”.
“Abstaining at 2nd reading gives May a massive lifeline. Brings amendments into play, so it’s game on again IF anything – Customs Union, EFTA, a second referendum etc – can muster a majority.”
Following local elections Jeremy Corbyn said the message was that Brexit needed to be delivered.
He said: “I think there’s a huge impetus on every MP – and they’ve all got that message, whether they themselves are Leave or Remain, or the people across the country – that an arrangement has to be made, a deal has to be done, parliament has to resolve this.”
Brexit secretary Steve Barclay acknowledged it would be the end of the road for the deal if the Withdrawal Agreement Bill is defeated.
He told the Lords EU Committee: “I think if the House of Commons does not approve the WAB then the (Michel) Barnier deal is dead in that form.”