Holding a new independence vote would be "a decision for Scotland" if the SNP win next May's Holyrood elections, Keir Starmer has said.
The Labour leader refused to say if he would try to block a second independence vote if Nicola Sturgeon gets a majority in the Scottish Parliament.
He told Sky News: "This is a question for Scotland, the people of Scotland. If there’s a majority it has got to be looked at in Westminster.
"But the Labour Party will be campaigning into May on the basis that what we don’t want is another divisive referendum."
Scotland voted to remain in the UK in 2014 but polls show rising support for independence - and Nicola Sturgeon plans to "make the case" for a second referendum from next year.
However, any second referendum would likely need to be given the green light by the UK government using a 'Section 30' order.
That suggests Boris Johnson could try to block it.
The SNP currently have 61 seats in the Scottish Parliament, just shy of a majority of the 129 available, but that could change in elections next year.
Asked by Sky News if, should the SNP win a majority, there should be another referendum, Sir Keir added: "That’s of course beyond May of next year.
"What I’m focused on... is talking about our priorities and our strategy for getting from here to May of next year and making the arguments that we think matter most, which are about the economy, public services and tackling the virus."
It comes after Wales' Labour First Minister, Mark Drakeford, said he would not stand in the way of a Welsh independence vote.
He told Sky News: "I am very clear that if a population in Scotland, or indeed in Wales, wanted to hold a referendum it is for the people of Wales and the people of Scotland to make that decision."
Sir Keir also said the December 31 Brexit transition deadline should not be extended - despite fears Boris Johnson will not strike a trade deal in time.
Earlier this year the Labour leader said "they should extend it if it’s necessary" but a legal deadline to extend the period has now passed.
Asked if it was now necessary, Sir Keir told the BBC today: "No.
"The two outstanding issues can be resolved.
"The Prime Minister said he’d got an oven ready deal, he needs to get on and he needs to deliver it. And if he fails to do so he needs to own that failure."
Asked if his party would back any trade deal, he said: "We will look at what comes back, but if it's in the best interests of the country, then we'll look at it, of course we will, because a deal is in the national interest."
Sir Keir - who pushed Labour towards backing a second referendum last year - added: "We have left the EU, we’re out, so the leave/remain argument is over."