The Daily Mail alleged on Monday that the Prime Minister told colleagues he would rather see "bodies pile high in their thousands" than impose a fresh wave of restrictions on England.
The remarks were reportedly made after Mr Johnson agreed to a second lockdown last year, and suggest he was prepared to face a mounting death toll rather than order a third set of tough restrictions - something he was eventually forced to do.
The decision on the second lockdown last autumn was leaked and is the subject of an inquiry to find the so-called “chatty rat” who tipped off the press.
The UK’s most senior civil servant is expected to indicate he has not cleared Mr Johnson’s former adviser Dominic Cummings over that leak, despite the ex-aide’s claims to the contrary.
The SNP’s Westminster leader, Ian Blackford MP, said Mr Johnson must come to Parliament to face questions from MPs on the “shocking” claims.
He said: "These comments are utterly abhorrent. If they are true, Boris Johnson has a duty to resign. The Prime Minister must now come to Parliament to give a statement, and face questioning, on these shocking claims and the growing Tory sleaze scandal engulfing Westminster.”
Downing Street has dismissed the Daily Mail’s report, based on testimony from an unnamed source, as “just another lie” - but it comes at an extremely uncomfortable time for Mr Johnson, who is struggling to face down accusations of sleaze over texts concerning the UK’s tax code that he exchanged with engineer James Dyson.
There is also an unfolding row over how he paid for the lavish refurbishment of his official No.10 flat.
Over the weekend, the International Trade Secretary Liz Truss insisted Mr Johnson had complied fully with the rules and had paid for the refurbishment, which reportedly ran to £200,000, out of his own pocket.
But during a round of broadcast interviews, she repeatedly refused to say whether the bill was initially settled by the Conservative Party, or one of its donors, in which case it should have been declared as a loan under party funding rules.
It is understood that Labour will ask Commons Speaker Sir Lindsay Hoyle to grant an urgent question requiring a minister to come to the House to respond to the charge that Mr Johnson plotted for Tory donors to secretly fund the work.
Mr Blackford said: "The public have a right to know what is going on, and why the Tory government has been handing out multi-million pound contracts, special access, tax breaks and peerages to Tory donors and friends.
"The difficulty for Boris Johnson is he has lied so many times it's impossible for anyone to trust a word he says.”
The member for Ross, Skye and Lochaber said an independent inquiry into the Prime Minister’s conduct was “the only way to provide transparency and accountability.”
He added: “Those responsible must be held to account."