Shadow chancellor John McDonnell has said a future Labour government would not block a second Scottish independence referendum.
In an interview with journalist Iain Dale at the Edinburgh Fringe Festival, Mr McDonnell said any decision about holding a vote would be up to the Scottish Parliament.
He said: "It will be for the Scottish Parliament and the Scottish people to decide that.
"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 view contradicts that of Scottish Labour leader Richard Leonard.
In an interview on the BBC's Sunday Politics Scotland in March, Mr Leonard said if Labour took power in Westminster the party would refuse to grant a "Section 30 order" giving Holyrood
the power to hold another vote.
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 on Tuesday: "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."
Scottish Conservative leader Ruth Davidson said: "John McDonnell's comments yesterday were met with complete dismay by Labour voters in Scotland.
"Today it's becoming clear why he said it. Labour is proposing a pact with the SNP in order to parachute Jeremy Corbyn into number 10.
"The fact is this - Jeremy Corbyn and John McDonnell would happily sell Scotland down the river if they thought it could give them a sniff of power.
"That is a rank betrayal of the two million Scots - including thousands of Labour voters - who voted to stay part of the UK.
"I can't imagine Scotland's Labour MP's were chuffed to hear Mr McDonnell describe Westminster as an 'English parliament'. It's not. It's a parliament for the whole UK with representatives from every corner of the country.
"With Jeremy Corbyn and John McDonnell doing Nicola Sturgeon's work for her, the First Minister must think Christmas has come early this year.
"Scottish voters can rest assured that the Scottish Conservatives will always stand up for our place in the United Kingdom and no Conservative prime minister would entertain doing a dodgy deal with the nationalists."