Labour has suggested Jacob Rees-Mogg should follow No10 aide Allegra Stratton out of the door after footage emerged of him joking about a Downing Street Christmas party.
The top Tory cracked a gag about police investigating the event last year at a Christmas bash hosted by the Institute for Economic Affairs thinktank.
In a video published by Guido Fawkes blog, the Commons Leader told the audience: "I see we're all here obeying regulations, aren't we?
"I mean, this party is not going to be investigated by the police in a year's time.
"You are all very carefully socially distanced... we have moved, I am pleased to tell you, from the metric back to the imperial system: I notice you are all at least two inches away from each other which is, as I understand it, what the regulations require."
No10 aide Allegra Stratton resigned yesterday over a leaked video showing Downing Street staff laughing and joking about how to describe the controversial event to journalists.
The footage, obtained by ITV, was said to have been filmed the week after the party took place on 18 December.
Mr Johnson finally "apologised unreservedly" for the party - after the Government repeatedly denied the Mirror's report that an event had occurred while the country was under strict Covid curbs.
But the PM continued to deny all responsibility and say he had been told rules were followed.
Downing Street aide Ed Oldfield, who took part in the mock press conference with Ms Stratton, refused to answer questions on Wednesday when doorstepped by journalists.
Labour's Thangam Debbonaire accused Mr Rees-Mogg of treating the row as a "bit of a joke" - and asked why Ms Stratton was being asked to "walk the plank".
The Shadow Commons leader said: "Judging by his comments as I saw on a video at a dinner earlier this week, it does rather seem that he also thinks it has all been a bit of a joke.
"After British people followed the rules and made their sacrifices... yes the PM's staff laughed about covering up their Christmas party but he also seems to think that it's funny."
She demanded to know why Mr Rees-Mogg didn't follow Ms Stratton's example.
Ms Debbonaire said: "Would he also agree that it really is a very bad look indeed for a group of male politicians to let a female staffer take the rap for the mess?
"She laughed, he laughed. She's apologised and resigned. What's he going to do?"
Mr Rees-Mogg said the Cabinet Secretary had been tasked with investigating alleged events in Downing Street last year - and defended his joke.
He replied: "As regards what I said at the IEA (Institute of Economic Affairs), what I was saying was how nice it was to be free of restrictions so that we can have parties this year.
"That was what I was being pleased about, as opposed, in comparison to last year. And this has got better because of what the Government has done."
He also paid tribute to Ms Stratton and said "she has left with great dignity".
Labour MP Richard Burgon said: "The Prime Minister's former spokesperson has resigned after being caught on video laughing and joking about a rule-breaking Downing Street party.
"The Leader of the House also this week has been caught on video laughing and joking about rule-breaking whilst giving a speech at a lectern.
"She resigned. Surely the Leader of the House should resign too, or isn't it another case of ministers in this Government believing it's one rule for them and another rule for everyone else?"
Mr Rees-Mogg replied: "I'm not sure he'd like to come to the Institute of Economic Affairs, it talks too much sense for him possibly to be able to cope with it.
"But he'd be very welcome to come to their future events and see what goes on and how nice it is, which I was celebrating, that we're back together having parties without restrictions.
"That is something that is extremely welcome."
