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But he announced on Thursday that he had formally withdrawn his letter to the committee, with the party also confirming that Mr Johnson would appear in person at the Scottish Conservative conference next weekend.
Mr Ross said he “had confidence in the prime minister to deal with this situation at the moment”, and that “everything else seems trivial” in comparison to the horrific scenes from Ukraine.
He added: “That is why I think our focus should be on supporting and helping the people of Ukraine, not on personal differences we may have with each other here in the UK.”
Other parties were critical of Mr Ross for withdrawing his call for the PM to go, with Scottish Labour leader Anas Sarwar saying Mr Ross “should not be using the Ukraine crisis to go back on his principles” and Lib Dem MSP Willie Rennie saying the Tory leader had “the backbone of a jellyfish”.
SNP Westminster leader Ian Blackford said it was “an utterly humiliating u-turn for Douglas Ross”.
But Mr Ross said he did not care about criticisms from other parties, and that the SNP had also been calling for unity just a few days ago.
He added: “They were standing up in the House of Commons saying we should work together, we should support the government because the threat is not here in the UK or between different political parties or the prime minister and the opposition.
“It is between the western world, Europe and allies across the globe and Russia – Vladimir Putin.
“That is the biggest threat at the moment, and that’s what our efforts should be united in trying to defeat.”
