Meanwhile, Andrew Bowie MP has written to the committee to request another vote of confidence after one was held last month.
In June, Ross spoke against changing the 1922 committee rules, stating he is a “stickler to the rules”.
The political storm rages on after leading UK Government cabinet figures chancellor Rishi Sunak and health secretary Sajid Javid quit.
Douglas Ross said: “The Prime Minister needs to realise he’s lost the support of many colleagues and he has to stand down as Prime Minister.
"It’s not an easy thing for many of us to tell the Prime Minister but the time is up and he needs to step aside.”
A Scottish Conservative spokesperson said Douglas Ross made his “position clear” on the Prime Minister in a vote of no confidence last month where he voted against the Prime Minister.
The spokesperson confirmed the Scottish Conservative leader’s opinion “hasn’t changed”, however, he was unable to confirm whether Ross would back a change in rules to allow another confidence vote.
Ross, who is an MP as well as leader of the Scottish Tories, previously called for Johnson to quit over PartyGate before performing a U-turn on the issue and then casting a no-confidence vote.
This morning, there have been more resignations, with junior minister Will Quince and ministerial aide Laura Trott both quitting.
The resignations come after the prime minister's handling of the row over Chris Pincher's appointment and what he knew about allegations against him has been criticised by opposition parties.
During a vote of no confidence last month, four out of six Scottish Conservative MPs voted to remove Boris Johnson as Prime Minister.
Joining Scottish Tory leader Douglas Ross in calling for Johnson to go were John Lamont, Andrew Bowie and David Mundell.
Andrew Bowie, MP for West Aberdeenshire and Kincardine, said: “Government is not functioning. I have therefore written to the 22 to request another vote of confidence in Boris Johnson's leadership.”
Only Scottish Secretary of State Alister Jack and MP David Duguid stood by the PM with Jack issuing a statement yesterday showing his continued support for Johnson.
The Scottish Secretary said: “I fully support the Prime Minister. I am sorry to see good colleagues resign, but we have a big job of work to do, and that’s what we’re getting on with.”
Some UK Government ministers are joining Jack in backing the Prime Minister, including Culture Secretary Nadine Dorries, Brexit Opportunities Minister Jacob Rees-Mogg, and Foreign Secretary Liz Truss.
This morning, Stephen Kerr, chief whip for the Scottish Tories in Holyrood said: “Yesterday was a busy and chaotic day. However, in the 300+ year history of the United Kingdom, it's just one more chapter.
"The UK is bigger than any person, Government, party, or policy- and people seeking to break it up off the back of any of those aren't being honest with you.
"The PM won a vote of confidence in his leadership last month and is safe from another vote for a year unless rules are changed”
BBC’s Good Morning Scotland reported on Wednesday that Douglas Ross, Alistair Jack or any Scottish Conservative MPs were unable to speak to them.
The SNP has demanded the Scottish Tories “break their silence” as the number of senior Tories resigning from the UK government rises even further.
Joe FitzPatrick MSP said: “Douglas Ross and his Scottish Tory colleagues normally need no encouragement to jump on the airwaves to defend Boris Johnson and his disastrous UK government. It’s telling that when the house of cards appears ready to fall, the media isn’t able to speak to any of them.
“In the last 24 hours, senior Tories have made it abundantly clear - they have no confidence in Boris Johnson. It’s time for the Scottish Tories to come out of hiding and face up to that reality too.
“While the Prime Minister clings on to save his political skin at the expense of Scotland and the whole UK, Douglas Ross could choose to support plans to oust the Prime Minister via the 1922 Committee. In the national interest, Scottish Tory MPs must now commit to backing these proposals.“With the full powers of independence, Scotland can rid ourselves of chaotic Westminster control once and for all. In the meantime, it’s time for Douglas Ross to tell the public whether he still supports a UK government led by Boris Johnson.”
Commenting, Scottish Labour deputy leader Jackie Baillie said: “The political odyssey of Douglas Ross continues apace, with yet another U-turn on the future of the Prime Minister.
“Mr Ross has been forced into performing into so many U-turns on this matter that he has sent himself and his party into tailspin.
“The facts are that Douglas Ross was more than happy to champion Boris Johnson as prime minister and prop up his dangerous government.
“Only Labour will pull our country together and lock Boris and the Tories out of power for good.”