Douglas Ross said there were "serious questions" to answer and the evidence suggests a party of some kind did take place, which was against the Covid rules.
Former Scottish Tory leader Ruth Davidson insisted the scandal was not “remotely defensible”, while Jackson Carlaw, her successor as leader, echoed Mr Ross’s call.
Mr Ross said he was angry at the way the issue had been handled and the public deserved answers.
However, he insisted he still had confidence in the Prime Minister.
It comes after Mr Johnson ordered an investigation into claims Downing Street staff broke lockdown rules by holding a Christmas party last year.
He told MPs he was “furious” about footage apparently showing aides joking about it.
The Prime Minister apologised “unreservedly” for the offence caused by the footage of his then-spokeswoman Allegra Stratton at a mock press conference.
But he said he had been repeatedly assured “there was no party and that no Covid rules were broken”.
Speaking at Prime Minister's Questions, Mr Johnson said he had asked Cabinet Secretary Simon Case “to establish all the facts and to report back as soon as possible – and it goes without saying that if those rules were broken then there will be disciplinary action for all those involved”.
Mr Ross told the BBC: "If the Prime Minister knew about this party last December, knew about this party last week, and was still denying it, then that is the most serious allegation.
"There is absolutely no way you can mislead Parliament and think you would be able to get off with that."
He added: “Misleading Parliament in that way is completely unacceptable and no one should continue in their post if they mislead Parliament in that way.”
Speaking to STV, the Scottish Tory leader said: "Clearly what we have seen over the last 12 hours or so with the video footage emerging, there are serious questions that need to be answered.
"Now looking at what I have seen, there was a party of sorts.
"I don’t think you can get away from that, and therefore questions have to be answered on why that was allowed as it was absolutely against the guidance this time last year."
He added: "That's why I think there are serious questions to be answered around what happened this time last year and what has happened in the last week to ten days as the Prime Minister has been answering questions in the House of Commons."
Mr Ross said everyone had made sacrifices last year.
He said: "People didn’t meet in the same way at Christmastime, they didn’t see their families as they would normally expect.
"They followed the guidance to the letter, in what was a united effort to get through this pandemic.
"If the people within Downing Street didn’t follow their own advice, then the appropriate action and strong action must be taken."
Mr Ross added: "I have confidence in the Prime Minister of the United Kingdom, but he and his Government have serious questions to answer on this issue."
He told Sky News the affair had “undoubtedly” damaged the Conservative Party.
The Scottish Tories leader said: “But more important for me than that – it’s not the political ramifications, I’ll deal with that or do whatever I have to do as the leader of the Scottish Conservatives.
“What angers me more is the families that had to sacrifice so much at the same time 12 months ago people thought it was OK to have a jolly in Downing Street.”
Ms Davidson tweeted: "None of this is remotely defensible.
"Not having busy, boozy not-parties while others were sticking to the rules, unable to visit ill or dying loved ones.
"Nor flat-out denying things that are easily provable. Not taking the public for fools.
"And today's 'we'll investigate what we've spent a week saying didn't happen and discipline staff for rules we continue to say weren't broken' was pathetic.
"As a Tory, I was brought up to believe in playing with a straight bat. Believe me, colleagues are furious at this, too."
Mr Carlaw told The Scotsman: “I’m quite happy to associate myself with what Douglas has had to say. I think that doesn’t pull its punches.”
Murdo Fraser, a long-serving Tory MSP and party frontbencher, tweeted: “Douglas speaks for all of us.”
There was widespread anger among Conservatives in Westminster and Holyrood.
One MSP told The Scotsman the events were “an absolute gift” for First Minister Nicola Sturgeon, adding: “It is Boris Johnson shooting himself in the foot, he is shooting himself and shooting us in the foot. It is so frustrating.
"It is the drip, drip, that does the damage ... this ducking and diving and not being straight.”
Another described it as a "self-inflicted wound" and insisted senior figures in the UK Government needed to “get a grip”.
Scottish Labour leader Anas Sarwar said: “I watched Boris Johnson at Prime Minister’s Questions today and, to be frank, he is a liar, he is corrupt and he is a joke – but the joke isn’t funny anymore.
“We are still in the midst of a pandemic. Lives are still being lost and lives are still at risk.
“At this time of national crisis, we need serious leadership. This is an out-of-touch, corrupt, lying government.”
SNP MSP Neil Gray said the Scottish Tories’ response to the scandal had been “utterly pathetic”.
He said: “Boris Johnson still has some very serious questions to answer and Douglas Ross’s flimsy attempts to distance himself from his own party, and the man he backed to be Prime Minister, just won’t cut it with the public.
“Instead of seeming more interested in saving the future of his Scottish Tory branch office than sticking up for decency and integrity in politics, Douglas Ross should find a backbone and join the SNP in calling on Boris Johnson to resign."