Sir Iain Duncan Smith, a former Conservative Party leader, raised the prospect during an event in Stirling in support of Liz Truss’s campaign to become the next prime minister.
He told party members: “We need to turn the tables on them and start saying ‘well, can we have a period of question time for you lot to talk about what you are doing in Scotland as the devolved administration?'
"And start examining some of this stuff because they're not just SNP protesters down in Parliament, they are actually part of the Government up here."
He said Tory ministers need to "take [the SNP's record in Government] apart on a regular basis, because it matters".
Aileen McHarg, professor of public law and human rights at Durham University, called the idea “completely constitutionally illiterate” and “fundamentally inconsistent with the principles of devolution”.
The SNP’s deputy Westminster leader Kirsten Oswald said: “This is an utterly ridiculous suggestion, showing that even the Tories are out of ideas for how to fix the broken Westminster system.
“It is not the SNP’s job to explain why Westminster control is increasingly making life more difficult for the people of Scotland – even if the Tories are out of excuses.
“The job of SNP MPs in Westminster is to stand up for Scotland against a UK Government choosing to ignore our interests at every turn.
"That is what they will continue to do for as long as we suffer under Westminster control, which I strongly believe won’t be for very much longer.”
Elsewhere, Sir Iain backtracked on Ms Truss’s recent comments that First Minister Nicola Sturgeon is an “attention-seeker” who is best ignored.
He said: "I don't want to ignore her. What I want to do is to let the world know just exactly why Scotland is suffering so much under this incompetent regime at Holyrood.
"The truth is, it is a disaster – everything from health, the police, the railways – they can't even build ships sometimes on time and on budget."
He said the "Union is in my blood and I believe it is in hers [Truss]".