The MSP said the scandal over the strategist’s trip from London to Durham during the lockdown is proving too much of a distraction.
Mr Carlaw said he had made his view that Mr Cummings should “consider his position” known to Downing Street, according to both the BBC and STV.
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If follows the resignation of Douglas Ross, the Under Secretary of State for Scotland, from the government over the issue.
Conservative MSP Adam Tomkins, a member of the Tories’ frontbench team at Holyrood, joined Mr Ross in calling for Mr Cummings to go and said other resignations may follow in the wake of the junior minister for the Scotland Office’s departure.
Mr Tomkins tweeted: “To lose (Douglas Ross) from government is a disaster. His was one of clearest voices for the Union in government. It shows exactly why Cummings should be sacked. I suspect others will follow where Douglas has led.”
In his resignation letter, Mr Ross said in his resignation letter: “I have constituents who didn’t get to say goodbye to their loved ones; families who could not mourn together; people who did not visit sick relatives because they followed the guidance of the government.
The Moray MP added: “I cannot in good faith tell them that they were all wrong and one senior adviser to the government was right.”
A No 10 spokesman said Mr Johnson “regrets’” Mr Ross’ decision to quit the government over the Mr Cummings row.
Another member of Mr Carlaw’s shadow cabinet at Holyrood, Graham Simpson MSP, has also called on Mr Cummings to go.
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“I don’t like calling for people to resign or to be sacked – there is too mu much of that. I tend to believe in giving people the chance to say sorry and learn. In this case I think Mr Cummings should go,” said Mr Simpson.
“He didn’t follow the advice that his own government, in which he is the key adviser, issued.”
Along with pressure from within his own party, Mr Carlaw has faced criticism from his political rivals in Scotland for failing to speak out on the issue. The Scottish Tory leader had said on Sunday he was satisfied Mr Johnson “reached a conclusion and we must all now focus on continuing to beat this dreadful pandemic”.
The SNP said Mr Carlaw’s defence of No 10’s position was “tone deaf”, while Labour accused him of “defending the indefensible”.
At least 25 Tory MPs have now either called for Mr Cummings to resign or for the prime minister to fire him.