Boris Johnson has told Nicola Sturgeon that he remains opposed to a second independence referendum, despite the SNP's general election success.
The PM spoke to the first minister by phone on Friday evening, with Downing Street saying he had "reiterated his unwavering commitment" to the union.
Mr Johnson insisted the result of the 2014 referendum "should be respected".
However, Ms Sturgeon made clear it was not "credible" to deny Scotland the right to choose its future.
Further talks agreed
She indicated during the phone call that she would be publishing a paper next week putting the case for a second independence referendum.
The two leaders have agreed to have a more detailed discussion in the near future over issues raised by an election result which saw the Conservatives take power at Westminster with an 80 seat majority and the SNP winning 48 of Scotland's 59 constituencies.
The nationalists won a landslide north of the border taking 13 more seats than in the last election in 2017 and seeing its share of the vote increase by 8.1 percentage points, to 45%.
In contrast, the Scottish Conservatives lost seven of their 13 seats in Scotland, despite Mr Johnson winning a majority of 80 across the UK as a whole - the largest majority for the Tories since 1987.
It means the UK is heading out of the EU at the end of next month, the BBC's political editor Laura Kuenssberg said, with Mr Johnson's "thumping" majority allowing him to get the laws required through Parliament "in a matter of weeks".
A Downing Street spokesman confirmed that the prime minister and first minister had spoken about both Brexit and a second independence referendum in their telephone conversation.
The spokesman added: "On Brexit, the prime minister said that he is now in a position to get this done in a way that allows the whole of the UK to move forward together, providing certainty for Scottish businesses and improving the lives of people right across Scotland.
"The prime minister made clear how he remained opposed to a second independence referendum, standing with the majority of people in Scotland who do not want to return to division and uncertainty.
"He added how the result of the 2014 referendum was decisive and should be respected."
Meanwhile Work and Pensions Secretary Thérèse Coffey ruled out any poll on Scottish independence for the full term of the Conservative government during an appearance on BBC Radio 4's Any Questions. - even if the SNP win a majority in the 2021 Holyrood election.
The conversation came after Mr Johnson spoke outside Number 10 of his hope that his party's "extraordinary" election win would bring "closure" to the Brexit debate and "let the healing begin".
And he insisted he was a One Nation Conservative, which he defined as "the idea that the Conservative Party should act for everybody in the UK. That means policies that work for people from different economic backgrounds, from different regions and from the different nations of the UK."
A spokeswoman for the first minister said it was a "constructive" phone call, "in which the [first minister] indicated she would be publishing a paper next week and the two leaders agreed to have a more detailed discussion in the near future over the issues raised by the election result".
She added that Ms Sturgeon had "made clear that it was not credible for the [prime minister] to deny Scotland the right to choose its future".
Speaking in Edinburgh earlier on Friday, Ms Sturgeon said that the SNP's "overwhelming" election victory in Scotland "renews, reinforces and strengthens" the mandate to hold another referendum.
She told Mr Johnson: "You, as the leader of a defeated party in Scotland, have no right to stand in the way. The people of Scotland have spoken. It is time now to decide our own future."
Ms Sturgeon said the Scottish government would be publishing a "detailed, democratic case" for letting Holyrood decide on whether there should be a second independence referendum.
She is expected to ask the UK government to transfer the legal powers to hold a referendum to the Scottish Parliament through what is known as a "Section 30 order" - as happened in 2014.
But she has repeatedly ruled out holding a referendum unless its legality was "beyond doubt".
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