The Scottish Secretary talked up Mr Ross on Thursday and rejected claims the party leader north of the border was a “lightweight”.
And Mr Jack revealed he had tried to talk Mr Ross out of calling immediately for Boris Johnson’s resignation before an inquiry into the Downing Street garden party was completed by senior civil servant Sue Gray.
It followed claims made by the Commons Leader, Mr Rees-Mogg, on Wednesday night.
Speaking to Radio Forth News, Mr Jack said: “Over the last 48 hours, I have, in a number of conversations with Douglas, asked him to wait until Sue Gray reports.
“She’s a serious figure, she’s producing a report. My view is we wait until we see the report before we draw any conclusions.
“I would say that Douglas is far from a lightweight.
“He’s a very serious politician, he’s a very good adversary for Nicola Sturgeon.
“Douglas is a very serious and, should be, [a] well-respected politician.”
Mr Rees-Mogg made the comments during an appearance on the BBC’s Newsnight programme, where he labelled Mr Ross “quite a lightweight figure” in the party.
Polling expert Professor Sir John Curtice said those comments “are going to get repeated endlessly north of the border” by the Tories’ opponents.
It came as Mr Rees-Mogg sidestepped calls from the SNP to issue a Commons apology to Mr Ross.
Speaking at business questions, SNP Commons leader Pete Wishart said: “The Scottish Tories know exactly how the rest of Scotland feels as the Leader of the House poured his scorn and contempt upon them last night.
“According to him, the democratically-elected Scottish Tory leader is an insignificant figure, a lightweight, a nobody – presumably just like every single Tory MSP who agree with their Scottish leader.
“The Scottish Tories are supposed to be the Praetorian Guard of the precious union and the Leader of the House has just undermined them and thrown them under the proverbial bus. If this is how the Government even treats the Scottish Tories, why should the Scottish people even entertain being any part of their useless union?
“Does he now want to take this opportunity to apologise to the MP for Moray for his remarks last night?”
Mr Rees-Mogg avoided answering the question, instead praising Mr Johnson’s “good, solid, decisive leadership” during the pandemic.
Speaking before entering Holyrood’s debating chamber for FMQs, Mr Ross dismissed the claims.
He said: “Jacob Rees-Mogg, as anyone, is entitled to their opinions. I don’t have to agree with them.
“My message is I’m going to hold the First Minister to account and ensure that Scottish Conservatives continue to provide a real alternative here in Scotland.”
Downing Street insisted on Thursday the Government was focused on action to “strengthen the union”.
The Prime Minister’s official spokesman was asked whether Mr Rees-Mogg’s comments undermined the efforts, and he said: “No, I think you can see what we’re doing on the union by what Michael Gove has set out just today on the review into inter-government relations, which seeks to take tangible action to strengthen our union.
“That’s very much been our focus.”