Douglas Ross has been branded a "coward" by the SNP for refusing to admit who he is backing to replace Boris Johnson.
Liz Truss and Rishi Sunak emerged this week as the last two candidates to survive a series of ballots by Tory MPs.
The winner will be decided by a postal vote of Conservative party members across the UK with the result announced on September 5.
But the leader of the party in Scotland has so far refused to endorse a single candidate and has insisted he is ready to work with whoever takes the top job.
In a statement, Ross said: "With the final two candidates having now emerged, I fully recognise that both of them bring extensive Cabinet service, particularly during some of the most challenging periods in the country’s history and either one of them are fully up to the task of being our next Prime Minister.
"As Scottish Conservative Leader, I will work with whoever emerges victorious from the vote by party members."
Ross was previously mocked by his political opponents after he called for Boris Johnson to resign as Prime Minister in January over PartyGate - only to perform a U-turn the following month.
SNP MSP Paul McLennan said: "The unfortunate Douglas Ross has once again demonstrated a complete absence of leadership qualities. He is too weak to say which of the candidates in the run-off would be the least bad for Scotland.
"He will do whatever the next UK Tory leader demands and instead of standing up for Scotland he is once again protecting the Tory party.
"We know he shot himself in both feet with his flip-flopping over Boris Johnson continuing his chaotic leadership, but it is now cowardice or contempt for Scottish voters if he simply won’t say who he prefers.
"As an MP, Ross voted in the five previous rounds before now so his refusal to declare his choice is untenable. In the interests of openness and transparency, he must say who he voted for at each stage.
"If he won’t say, is it because he knows that every one of the original candidates – including the final two – will be another disastrous Prime Minister who will inflict untold damage on the people of Scotland?"
The Record revealed today how no Scottish Tory MP has publicly endorsed the bookies’ favourite to be the next Conservative Prime Minister
Liz Truss is struggling to win the support of parliamentarians north of the border, with only one MSP so far backing her.
It came as former Scots Tory leader Ruth Davidson backed Truss rival Rishi Sunak for the top job.
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