Mark McDonald, who has already quit as a Government minister, announced his resignation from the SNP yesterday - but said he intends to stay on as an Independent MSP.
But the First Minister yesterday backed opposition calls for the former children’s minister to resign his Holyrood seat and give his constituents the chance to elect a new MSP.
McDonald yesterday issued an “unreserved apology” to three women who complained about his behaviour and said he had been seeing a behaviour coach.
But Ms Sturgeon said: “The SNP cannot force Mark McDonald to stand down as an MSP.
“So it’s a matter for him. My view is clear - he was elected as an SNP MSP and if his behaviour was such that he himself considers that he cannot continue as an SNP MSP then it would be appropriate to give his constituents the opportunity to elect a new MSP.”
Mr McDonald’s resignation came on the eve of a scheduled disciplinary vote by his Holyrood colleagues to determine his future in the SNP group.
There is no suggestion that his behaviour was serious enough to merit a police investigation.
But his decision to remain prompted an angry reaction from opposition MSPs who questioned how his behaviour was bad enough to see McDonald quit the SNP - but not Parliament.
Tory MSP Alexander Burnett said: “Many people will rightly be questioning why Mark McDonald thinks that his behaviour was bad enough to resign from the SNP, but not to resign from the Scottish Parliament.
“He is clearly prioritising the reputation of the SNP over that of Holyrood, and it’s simply not good enough.”
Mr McDonald announced his resignation in a statement in Aberdeen where he refused to take questions.
He said his behaviour coach had made him a better person and he has been assessed as showing a “willingness to change”.
He added: “I would like to take the opportunity to offer a public and unreserved apology to those individuals for the hurt and offence that I have caused them.”
He also revealed that had sent a written apology to one of the complainers, in line with that individual’s wishes.
The probe found that Mr McDonald had sent “inappropriate and unwanted” text and social media messages, as well as causing distress as a result of his “unwanted attention”.
The behaviour was also found to be “persistent over an extended period of time”. He was also judged to have “exploited his position of power”.
A further allegation of “inappropriate physical contact” during a social event in Edinburgh could not be established.
Labour’s Parliamentary Business Manager Rhoda Grant said: “Mark McDonald decided his conduct was not fit for a minister or an SNP MSP - but somehow it is acceptable for an MSP without party affiliation.
“People in Aberdeen Donside will rightly question that. It looks like Mark McDonald has put the reputation of the SNP before what is best for his constituents.”
Mr McDonald said he would be returning to Parliament next week and Holyrood authorities said yesterday they would be discussing “practical arrangements” for this.
There are currently no other Independent MSPs sitting at Holyrood.