The First Minister is the focus of an investigation over whether she misled the Scottish Parliament on when she knew about allegations of harassment made against her predecessor Alex Salmond.
Ms Sturgeon said she first learned of the complaints in a meeting with Mr Salmond at her home in early April 2018, but it later emerged she had been told by his former chief of staff in her Holyrood office a few days prior, a fact she claims to have forgotten.
She referred herself for investigation by James Hamilton QC, an independent adviser on the ministerial code.
If Ms Sturgeon is found to have broken the ministerial code, Mr Sarwar said she should step down, saying she would expect the same of ministers in other parties.
“If there is a minister, forget who the minister is or what political party they are from, if a minister is found to have breached the ministerial code, I think people would expect that minister to resign,” the newly elected Scottish Labour leader told Sky News’ Sophy Ridge On Sunday.
“That’s what Nicola Sturgeon would say if it was a Labour politician, a Conservative politician or a Liberal Democrat politician, so let’s take the party politics out of it – it’s a point of principle.”
When pushed specifically on whether or not the First Minister should step down, Mr Sarwar said: “Yes, I think Nicola Sturgeon herself would say that if an opposition politician was in government and they’d breached the ministerial code, they would be expected to resign.
“Let’s take the party politics and the personalities out of it, it’s a point of principle and respecting the office of First Minister.”
Speaking in his first broadcast interview since becoming leader on Saturday, defeating Monica Lennon with more than 57% of the vote, Mr Sarwar said he believes the First Minister would not support touting a referendum on independence if it were not for the internal struggles of the SNP.
Factions within Scotland’s ruling party have grown more impatient with the approach to independence in recent months, as well as internal strife on the issue of transgender rights and the ongoing Salmond inquiry – where the former first minister claims there has been a “malicious and concerted” effort to push him out of public life from the highest echelons of the party.
The Glasgow MSP said: “The idea that we come through (the Covid-19 pandemic) and straight into a divisive referendum campaign, I just don’t think it’s the right thing to do – instead I think it’s right that we focus on rebuilding our country.”
He added: “I actually don’t think even Nicola Sturgeon would be advocating a referendum right now, but I think she’s more focused on healing the wounds in her political party than she is about healing the wounds in the country.”