Douglas Ross was speaking for the first time after withdrawing his call for the PM to quit over Downing Street parties.
Mr Ross said the row over the lockdown parties now seemed trivial in comparison to the Russian invasion of Ukraine.
And he said now would be “totally the wrong time” to change leader.
He acknowledged that there would continue to be personal differences between himself and Mr Johnson, but said his position on the prime minister’s leadership during the Ukraine crisis was very similar to that of Labour leader Sir Keir Starmer.
Mr Ross said: “Now is not the time to try and replace a prime minister – now is the time for unity.
“The only person who would gain from the removal of a UK prime minister from office would be Vladimir Putin.”
Mr Ross warned that the Russian president would use any signs of division as a “wedge” to drive between the forces that are trying to stop him.
The Scottish Conservative leader had written to the 1922 Committee of backbench Tory MPs in January to express his lack of confidence in Mr Johnson and to call for a leadership contest.
Mr Ross described the prime minister’s position at the time as “untenable” after he admitted attending a Downing Street party during the Covid lockdown.
But he announced on Thursday that he had formally withdrawn his letter to the committee, with the party also confirming that Mr Johnson would appear in person at the Scottish Conservative conference next weekend.