The Scottish Labour leader challenged his Tory counterpart after Mr Ross supported a motion of no-confidence in the Prime Minister on Monday.
Speaking on Tuesday, the MP on Moray claimed Mr Johnson should “look at” resigning.
He added: "This isn't just some Scottish MPs, some Welsh MPs, a few from a certain part of England.
"This is across the entire parliamentary party – from people who supported staying in the EU and people who campaigned strongly to leave the EU, people who are on the right of the party, some in the centre and some on the left."
Now Mr Sarwar has criticised Mr Ross for changing his mind over the Prime Minister and asked if he will support Mr Johnson at a general election.
In a letter, Mr Sarwar said: “Voters have a right to expect their politicians to show integrity, consistency, and honesty. As leader of the Scottish Conservatives, you have adopted six different positions on rule breaking and the leadership of Boris Johnson.
“Now, the Scottish Conservatives must come clean. Will you personally campaign for Boris Johnson at the next election? Will the Scottish Conservative Party campaign for Boris Johnson to remain as Prime Minister at the next general election?
"Surely you and your party cannot, in good conscience, campaign for a man who you have no confidence in?”
Scottish Conservative Party chairman Craig Hoy dismissed the letter and claimed Labour had “betrayed pro-UK voters”.
He said: “Anas Sarwar can’t lie to pro-UK voters about coalition deals with the SNP then try to talk about honesty and integrity.
“They refused to work with other parties to lock the SNP out of power in councils across Scotland, then did a coalition deal to put the SNP into power, just a few months after Anas Sarwar promised not to do exactly that.
“In the next general election, pro-UK voters won’t trust a word that Anas Sarwar says. They know Labour will do a deal with the SNP if they get the slightest whiff of power.
“A lot can happen before the 2024 general election, but the man who campaigned to put Jeremy Corbyn into Downing Street doesn’t have a leg to stand on.”