Mr Blackford welcomed the former London Mayor to his post by challenging him over his mandate - while Mr Johnson accused the SNP's Westminster leader of pessimism.
Mr Blackford said: "It's often said the Prime Minister lives in a parallel universe - that's been proven beyond any reasonable doubt this morning."
The Skye MP called on Mr Johnson to hold a general election, a suggestion to which Mr Johnson replied: "The people of this country have voted in 2015, 2016, 2017 - what they want to see is this Parliament delivering on the mandate they give us, including him."
Mr Johnson labelled Mr Blackford's question indicative of his "defeatism and pessimism", adding: "If we can deliver a fantastic, sensible and progressive Brexit, which I believe we can, and the whole United Kingdom comes out, as I know that it will, what happens then to the arguments of the Scottish National Party?
"Will they seriously continue to say Scotland must join the Euro? Will they seriously suggest that Scotland must submit to the entire panoply of EU law?"
Backbench SNP MPs Stewart McDonald and Deirdre Brock asked Mr Johnson pointed questions about his dealings with Russian oligarchs and Cambridge Analytica rspectively.