A future Labour government would not block a second Scottish independence referendum, according to shadow chancellor John McDonnell.
In an interview at the Edinburgh Fringe Festival, he said any decision about holding a vote would be up to the Scottish Parliament.
His view contradicts that of Scottish Labour leader Richard Leonard.
Earlier this year, Mr Leonard said the party would refuse to grant Holyrood the power to hold another vote.
Mr McDonnell's comments follow the publication of an opinion poll suggesting the majority of Scots could back independence.
And on Monday Nicola Sturgeon told journalist Iain Dale there was a "growing urgency" for Scotland to become independent "sooner rather than later".
Mr McDonnell was also speaking to the LBC broadcaster when he was asked about the possibility of a second independence vote.
"It will be for the Scottish Parliament and the Scottish people to decide that," the senior Labour MP said.
"They will take a view about whether they want another referendum. Nicola Sturgeon said by late next year or the beginning of 2021."
He added: "We would not block something like that. We would let the Scottish people decide. That's democracy.
"There are other views within the party but that's our view."
Mr McDonnell's position appears to be in opposition to the leader of the Scottish Labour party.
In March, Richard Leonard told the BBC's Sunday Politics Scotland that if Labour took power in Westminster the party would refuse to grant a Section 30 order.
He added: "What we said in the manifesto at the 2017 election was that there is no case for, and we would not support, a second independence referendum."
However, Mr McDonnell said: "The Scottish Parliament will come to a considered view on that and they will submit that to the government and the English Parliament itself.
"If the Scottish people decide they want a referendum that's for them."
His comments were condemned by his party colleague Ian Murray, the MP for Edinburgh South.
"These are utterly irresponsible comments from John McDonnell that betray our party's values," he said.
"The Labour Party is an internationalist party founded on a vision of solidarity and we should never seek to appease nationalists, whether they be for Brexit or Scottish independence, who want to divide communities and people."
In a post on Twitter Nicola Sturgeon said the Shadow Chancellor's position was "basic democracy".
She added that it made "political sense" as polls suggested 40% of Labour voters support independence.
John McDonnell’s position on #indyre2 is a statement of basic democracy - but given poll showing 40% of Labour voters support independence it also makes political sense. @scottishlabour reaction goes some way to explaining the existential crisis they face.— Nicola Sturgeon (@NicolaSturgeon) August 6, 2019
Meanwhile, Scottish Liberal Democrat leader Willie Rennie described Mr McDonnell's comments as "astonishingly irresponsible".
"It's bad enough with Boris Johnson bungling on Brexit and independence but to have the Labour Party's chancellor piling in makes it a whole lot worse," he said.
'We want to change the world'
On Brexit, Mr McDonnell said Labour leader Jeremy Corbyn would "never" step down if other opposition parties demanded it to form a coalition of national unity.
He said: "It won't happen. I think we'd form a minority government, seek to implement our manifesto and we'd expect the other opposition parties and other MPs to vote for those policies and if they don't we'll go back to the country.
"If they want to vote against a real living wage, if they want to vote against £70bn worth of investment in Scottish infrastructure, if they want to vote against a green industrial revolution to tackle climate change then so be it, we'll go back to the people and then let them explain to the people why they wouldn't support those policies."
"We want to change the world, we're not going be held back by other parties."
The senior Labour frontbencher said he was "extremely worried" about new Prime Minister Boris Johnson.
He added: "I think he's reckless and I think he's unstable and I will move heaven and Earth to stop a no-deal Brexit."