Keir Starmer has agreed to face-to-face talks about an independence referendum, John Swinney’s government claimed on Tuesday night.
It followed the First Minister and Prime Minister having a short call about the election.
Mr Swinney raised the record number of pro-independence MSPs at Holyrood and their demand for a referendum.
According to Scottish Government sources, the Prime Minister repeated his opposition to separation, but agreed to discuss the issue and other topics next month.
Downing Street insisted its position ‘remains unchanged’.
The Scottish Conservatives warned throughout the election that Sir Keir was too weak to stand up to the SNP if the Nationalists demanded a vote on breaking up Britain.
Although Mr Swinney fell short of his target of an SNP majority, his 58 MSPs plus 15 Greens makes 73 Nationalists in a parliament of 129.
Scottish Tory leader Russell Findlay said: ‘Even by Sir Keir Starmer’s dismal standards this would be an extraordinary capitulation to John Swinney.
‘For Starmer to entertain talks on the subject when the Nationalists haven’t even met their own target is downright foolish and reckless.’
In a statement, the SNP Government said Sir Keir congratulated Mr Swinney on his win in the 10-minute call and offered ‘to work collaboratively wherever possible’.
Keir Starmer had a short conversation with John Swinney
Swinney is determined to push for second independence referendum
It went on: ‘The First Minster set out the majority of MSPs were elected on a commitment for a referendum on Independence and that this number was now at record levels.
‘He highlighted comments by MSPs from the Prime Minister’s party in support of the need for a way to resolve this question.
‘The Prime Minister and the First Minister agreed to a face-to-face meeting next month to discuss these issues, ahead of a meeting of the leaders of all four UK nations. Dates will now be agreed.’
Glasgow Labour MSP Paul Sweeney this week floated a cross-party constitutional convention to examine the trigger for a referendum.
He said: ‘We need to get beyond this paralysis to allow politics to function properly again in Scotland, so perhaps it does need to be settled in some sort of convention.’
A Downing Street spokesman said: ‘The PM committed to meeting to discussed shared issues including the cost of living.
‘As the PM told the First Minister, the manifesto this government was elected on was unambiguous that “Labour does not support independence or another referendum”.
‘Our position remains unchanged.’
UK Health Secretary Wes Streeting, who could soon replace Sir Keir, recently ruled out the 'chaos' of a referendum, telling the SNP: 'They're not having one.'