Boris Johnson has denied fuelling the break up of the UK after reportedly saying devolution was a "disaster".
Sir Keir Starmer - who shares the PM's opposition to Scottish independence - seized on the alleged comments at Prime Minister's Questions.
"The single biggest threat to the future of the United Kingdom is the prime minister every time he opens his mouth," the Labour leader told MPs.
The PM is said to have made the remarks in a call with Tory MPs on Monday.
He told them devolution - setting up separate Parliaments in Scotland, Wales and Northern Ireland - was "a disaster north of the border" and "Tony Blair's biggest mistake".
Sir Keir described devolution as "one of the proudest achievements of the last Labour government".
He said the PM's alleged remarks were not an "isolated incident" and accused him of "seriously undermining the fabric of the UK".
"Does he agree that we need greater devolution across the UK?" asked the Labour leader.
The prime minister said devolution was a "sound policy", which he himself had benefited from as mayor of London, but the SNP had turned it in to "a mission to break up the UK".
"That, in my view, would be a disaster," he added.
He was then told off by Commons Speaker Sir Lindsay Hoyle for referring to the SNP as the "Scottish Nationalist Party".
Sir Lindsay said: "Can I just say it's the Scottish National Party, not the nationalist party."
Mr Johnson replied: "Mr Speaker, I'm so sorry. They're national but not nationalist. I see, right."
The SNP's Westminster leader Ian Blackford said the prime minister's "attack on devolution" was "not just a slip of the tongue, it was a slip of the Tory mask".
"The fact is Scotland has been completely ignored by Westminster. We now face an extreme Brexit, a power grab and another round of Tory cuts all being imposed against our will by a Tory government that we didn't vote for."
The prime minister told Mr Blackford he was "totally wrong" and "what the UK does as a whole is far, far bigger, better and more important than what we can do as individual nations and regions," such as the furlough scheme and coronavirus testing.
He said he wished the Scottish government would "focus on the real priorities of the people of Scotland", such as health and education.
Former Labour prime minister Gordon Brown has, meanwhile, warned the UK will follow the British empire "into the history books" within a decade if it does not embrace reform.
Mr Brown claimed the pandemic had shown parts of the UK were being imprisoned in what he called "the straightjacket of a unitary state" - and that Whitehall had been "inflexible" and "insensitive".
Writing for the New Statesman, he also admits it was naive of Labour not to acknowledge devolution would create "a megaphone for intensifying resentment".
But he says the current issue is not just in Scotland or Wales, but UK-wide, with regions needing more power.
He argues for a formalised "Council of Nations and Regions" and for the Lords to be replaced with a Senate of the Nations and Regions.
He writes: "The pandemic has revealed what has long been true: either we reform and renew and survive, or we resist and refuse and, in ten years' time, having failed to act, the United Kingdom will follow the British Empire into the history books as an anachronism whose time has passed."