Scotland Correspondent Peter Smith says that neither Boris Johnson or Nicola Sturgeon want an independence referendum at the minute as the issue is "balanced on a knife edge"
Earlier in the day, Scotland's first minister said any move to block a second referendum would mean Westminster would be “saying the UK is no longer a union based on consent”.
The SNP is one seat short of an overall majority after the Scottish parliament elections, but the final result still leaves Holyrood with a pro-independence majority.
A Downing Street statement following the phone call between the two leaders did not mention a referendum, instead focusing on unity between the different parts of the United Kingdom and highlighting the need to work together to overcome the Covid pandemic.
A spokesperson for Nicola Sturgeon confirmed that she too agreed "that her immediate focus was on steering the country through Covid and into recovery, and that a newly elected Scottish Government would work with the UK government as far as possible on that aim".
Yet they went on to say: "The first minister also re-iterated her intention to ensure that the people of Scotland can choose our own future when the crisis is over, and made clear that the question of a referendum is now a matter of when - not if."
However, a spokesperson for Boris Johnson played down the calls for a referendum, instead saying the PM had "congratulated" Ms Sturgeon on her victory.
They continued: “They both agreed that their immediate focus should be and is on working together to build back from the pandemic.
"The prime minister stressed how recovery will be more effective if both governments work together and reiterated his invitation for the first minister to join a summit meeting to discuss our shared challenges on Covid recovery and how we can overcome them.
“The prime minister also discussed other areas of shared interest as a strong United Kingdom, including setting the green agenda and the COP26 Summit in Glasgow.
“The prime minister concluded by emphasising the importance of focusing on Covid recovery at this time.”
The statement from Downing Street follows a letter Mr Johnson sent to Ms Sturgeon on Saturday, following victory for the pro-independence movement at the polls, inviting the leaders of the devolved nations to the summit on crisis talks on the Union.
In the letter the PM said: “We will all have our own perspectives and ideas – and we will not always agree – but I am confident that by learning from each other we will be able to build back better, in the interests of the people we serve.”
Speaking to ITV News on Sunday, Cabinet Office minister Michael Gove echoed the prime minister in his focus on the UK's need to unite in order to recover from the coronavirus pandemic.
When asked when he thought any referendum could take place, Mr Gove replied: “Not now" and refused to be drawn on when one could take place, saying it would be a "distraction" from the Covid recovery.
Earlier on Sunday, Ms Sturgeon appeared on the BBC's Andrew Marr Show, where she said it was “up to the Scottish people” to decide the country’s future and if the referendum was blocked Scotland would be "retained in that union by force of law”.She said she hoped a bid for a second referendum would not end up in court because that would mean "a Conservative government had refused to respect the democratic wishes of the Scottish people".
Ms Sturgeon added: “The fact that we are sitting here having a debate about whether or not that outcome is going to be respected says a lot about the lack of respect for Scottish democracy that this UK government has demonstrated for quite some time now.”In her victory speech on Saturday Ms Sturgeon told supporters the result proved a second independence vote was the “will of the country” and said any Westminster politician who stood in the way was “picking a fight with the democratic wishes of the Scottish people”.
The SNP leader immediately promised Scots an IndyRef2 vote and she dared the PM to stop her, ITV News Scotland Correspondent Peter Smith reports
Also speaking on Sunday morning, Mr Gove said the UK and Scottish governments should “concentrate on the things that unite us” rather than “constitutional wrangling” over a second independence referendum.He told Sky News' Sophy Ridge of Sunday: "Instead of concentrating on the things that divide, let’s concentrate on the things that unite and let’s concentrate on all of us to work together to serve the people that just vote for us.”
He said the SNP's focus on securing a second referendum "was “a slightly skewed set of priorities to imagine that that is the most important issue” in the light of the pandemic recovery."
Mr Gove also dodged questions on what the government would do if Holyrood submitted an official request for a second referendum saying "we are not going to go there.”
He also noted when Alex Salmond secured a majority for the SNP in 2011 every Scottish political party agreed there should be a referendum and this is not the case now.
Communities Secretary Robert Jenrick stressed that, despite the strong preference in Scotland for pro-independence parties, it would be a “grave error” to pursue another border poll.
The Cabinet minister told BBC News: “I don’t know what the future might hold but our sole focus right now must be on recovery, and I think being distracted in any way by talk of constitutional wrangles would be a grave error.”
Meanwhile, Welsh Labour responded to the letter by saying it would would welcome a Union summit if it is “real”, a minister said. On Sunday, Welsh Labour housing minister Julie James was asked about Mr Johnson’s proposal to have a “Team UK” summit and approach to coronavirus. She told BBC Politics Wales: “I hope very much that it’s real. We would welcome it if it was. “We’ve been calling for many, many years for a proper constitutional summit, where we talk properly about the role of devolution across the UK, in a United Kingdom. “We very much welcome that. You’ve heard party leaders from us for many, many years saying how necessary that is.” Ms James added that where devolution exists, there is a “clear appetite for it”.
The dispute over a follow-up referendum came as Labour recriminations began over its poor showing in the Super Thursday elections on Thursday.
Deputy Labour leader Angela Rayner was sacked on Saturday from her role as chair and national campaign coordinator.
It comes after the Opposition outfit lost the Hartlepool by-election – with the North East town voting for a Tory MP for the first time in 60 years – and incurring a net loss of six councils and more than 200 seats in the local elections as voters in its traditional heartlands deserted the party.
Prominent figures on the left of the party hit out at the move, with former shadow chancellor John McDonnell calling it a “cowardly avoidance of responsibility” by leader Sir Keir Starmer.
The row came despite Labour faring better in Saturday’s results, producing surprise victories in the West of England and Cambridgeshire and Peterborough mayoral contests, while comfortably winning second terms in Greater Manchester and the Liverpool City Region with Andy Burnham and Steve Rotheram respectively.
Mr Burnham – who has been installed as the bookmakers’ favourite to replace Sir Keir, despite not being an MP – did not close the door on the possibility of becoming the next Labour leader, saying: “In the distant future, if the party were ever to feel it needed me, well, I’m here and they should get in touch.”
In London, Labour’s Sadiq Khan had to wait late into the night to find out that he had won a second term as mayor in City Hall after fending off a challenge from Tory rival Shaun Bailey, and Marvin Rees won a second term as Bristol mayor for Labour, beating Green candidate Sandy Hore-Ruthven in the run-off after the Liberal Democrat and Conservative candidates were eliminated.
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Mr Johnson vowed there would be “no let up in levelling up” after his successful further dismantling of Labour’s so-called “red wall”, adding: “Voters have put their trust in Conservative representatives, councillors and mayors and we must deliver for them.”
Mark Drakeford’s Welsh Labour avoided the kind of electoral drubbing Sir Keir endured on Friday.
With the final declarations made on Saturday, Labour ended with exactly half the 60 seats in the Senedd – one short of an overall majority – equalling its best ever results.
First Minister Mr Drakeford, who extended the majority for his Cardiff West seat by more than 10,000 votes, vowed to be “radical” and “ambitious” in government.