Scottish independence: Labour 'will grant indyref2' - under one condition
Shadow Business Secretary Rebecca Long-Bailey said Labour "wouldn't try and stop" indyref2 if the Scottish Government wanted one at that point, but would not agree to one earlier.
Her party's latest position on the issue emerged as Boris Johnson ruled out granting permission for a re-run of 2014's referendum while he was Prime Minister.
The Conservative leader insisted there was no reason to go back on assurances given by the SNP that the previous referendum would be a "once in a generation" event.
Indyref2 crucial to election
The issue of indyref2 is set to be a crucial factor in deciding the result of the general election in Scotland, with Ms Sturgeon putting her demand for a 2020 vote at the "heart" of her message.
The SNP leader has said she is confident that Labour will agree to allow a referendum on her timetable if Jeremy Corbyn enters Downing Street after 12 December.
However, the Labour leader has insisted he is against Scottish independence and would not transfer the necessary powers for a legally-binding poll until 2021 at the earliest.
Asked about the issue on Sunday, Ms Long-Bailey said her party's position was to wait until after the 2021 Holyrood election before granting a Section 30 order.
"After the next Scottish Government elections, if the Scottish Government determine they want to pursue another referendum and they go through the legislative process within their own government to push that forward, than as a government we wouldn't stand in their way," she told Sky News.
This means that if Labour win next month's election, the SNP will have to get through the 2021 election with a pro-independence majority before any vote will be granted.
However, Mr Corbyn may have to compromise on this timetable if he fails to win the election and needs to do a deal with Ms Sturgeon to prop up a minority Labour government.
Ms Sturgeon said the SNP winning a majority of Scotland's seats next month would represent a mandate for a referendum in 2020, the timetable she prefers.
"For any Westminster politician to seek to stand in the way of an independence referendum on that timescale would be seeking to ignore the democratically-expressed wishes of the Scottish people," she added.
But when asked if he would grant permission for such a ballot while he was Prime Minister, Mr Johnson said: "No, I don't want to have one."
SNP Westminster leader Ian Blackford claimed that the other main UK parties were "buckling under the pressure of what is a democratically unsustainable position" on indyref2.
“Senior Tories no doubt realise that what goes down well in the Tory conference hall will go down like a bucket of cold sick on Scotland’s doorsteps in an election campaign," he added.