SNP Westminster leader Stephen Flynn said language used by Professor Jason Leitch in WhatsApp messages would “make most people uncomfortable”.
Prof Leitch, a prominent Scottish Government adviser, branded a Conservative politician “rude” and a Labour MSP a “smart-arse” after giving a coronavirus briefing in June 2021.
The messages were part of an exchange with then-Health Secretary Humza Yousaf, and were published by the UK Covid-19 Inquiry.
Prof Leitch, who is a civil servant, also called a newly elected Labour MSP, Mercedes Villalba a “new girl” after she was elected to Holyrood that month.
In a previous exchange, in May 2021, Prof Leitch said he could “barely understand” Scotland’s chief medical officer, Professor Sir Gregor Smith.
The Scottish Conservatives condemned “mudslinging” at opposition politicians, and called for Prof Leitch “to do the decent thing and resign or be sacked as national clinical director”.
Speaking to the BBC, Mr Flynn said “some of the language that has been used most people would probably be relatively uncomfortable with” but did not call for an apology.
He also said he was “thoroughly impressed with the job they did”.
Mr Flynn said: “It’s not for me to pass comment or judgment on the role of a civil servant but I’m sure Jason Leitch will be reflecting heavily on it and I’m sure if he wants to say something in relation to it he will to the people of Scotland.
“I think given some of the language that has been used most people would probably be relatively uncomfortable with it and it’s for Jason to determine himself which course of action he wants to take.”
He added: “I don’t think it would be unreasonable for people to expect someone who has used that terminology to apologise to those involved.
“But I also think we need to remind ourselves that the Scottish Government did work on all of our behalf. Nicola Sturgeon was on the TV every day reassuring us throughout the pandemic, trying to do the very best to make sure we were all safe.
“I was thoroughly impressed with the job they did. It certainly helped me and my family cope with what was a very challenging set of circumstances.
“And that was in stark contrast to what we saw emanating from Westminster with comments like let the bodies pile high.”