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New Prime Minister Andy Burnham is reported to have told Scotland's First Minister John Swinney that they will have to "agree to disagree" on Scottish independence.
The two leaders spoke on the phone on Tuesday morning for the first time since Burnham took office.
Swinney raised the issue of Scotland's future, stressing the pro-independence majority in Holyrood, in the hope of advancing the debate.
But a UK government source told the Press Association that the prime minister had been resistant.
He said: "When the question of independence was raised, the prime minister was quite firm they would have to agree to disagree.
"It's not something he's focused on and it's not a conversation that he's interested in taking forward."
The source described the rest of the call as "quite warm and constructive".
He added that Burnham emphasised to Swinney the areas where the two governments could work together and spoke of his drive for a "new kind of politics".
Last week Swinney congratulated the former mayor of Greater Manchester after he was confirmed as UK Labour's new leader.
He said he hoped to build a "constructive relationship" with Burnham that would improve the lives of people in Scotland.
Following the phone call on Tuesday, a Scottish government spokesperson said: "He [Swinney] set out his commitment to both governments working constructively together to address the cost-of-living crisis and to lower energy bills.
"The first minister set out the majority within the Scottish Parliament for the future of Scotland to be decided by the people of Scotland and looked forward to a constructive dialogue on this issue."
According to the spokesperson, Swinney also used the call to extend an invitation to the PM to visit Scotland.
On his first full day in the job, Burnham also spoke to the leaders of Wales and Northern Ireland.
A Downing Street spokesperson said he stressed his desire for "practical measures, not constitutional changes like further referendums".
The spokesperson said: "The prime minister said he was serious about creating a new politics - rooted in finding common ground based on collaborative, practical and pragmatic relations with the heads of the devolved governments.
"Working in partnership, the prime minister said together they could drive deeper devolution to all parts of the United Kingdom to get growth going.
"The prime minister added he was focused on practical measures, not constitutional changes like further referendums, to give families more breathing room by helping them with the cost of living, which he had done today by helping millions of households with their energy bills."
