The First Minister has suggested the Scottish Parliament must act to reassure staff following claims made by human rights lawyer Aamer Anwar at the weekend.
He claimed to know of a “catalogue” of cases at Holyrood which cut across all parties.
Ms Sturgeon has now written to Holyrood Presiding Officer Ken Macintosh calling for action.
“Any such behaviour is absolutely reprehensible and must be addressed,” Ms Sturgeon said.
“We cannot and must not be complacent about the position at Holyrood. We need to do everything in our power to make sure that the Scottish Parliament is a workplace where there is zero tolerance of such unacceptable behaviours.
“As part of that, it is vital to ensure that robust procedures are in place so that individuals who raise concerns have confidence that they will be fully investigated in an appropriate manner. Indeed, we should expect a similar standard of protection to exist in every place of work across Scotland.
“The existing Code of Conduct for MSPs is clear that it is unacceptable for MSPs to subject staff to sexual harassment.
“However, in light of these recent developments I would be grateful to learn what additional steps the Parliament might consider taking to strengthen the level of reassurance for staff and all others who come into contact with Parliament.
“t may be that convening a cross party meeting would be one way to review the current arrangements and to offer recommendations on how these might be strengthened.”
Tory leader Ruth Davidson has also ordered a review of the way her party deals with abuse complaints in light of the harassment claims.
The Edinburgh Central MSP said: “The allegations that have emerged in recent days are deeply troubling.
“Sexual harassment in the workplace is wrong and must not be tolerated. Those in positions of power, like MPs and MSPs, have an even greater responsibility to lead by example and show respect for all members of staff.
“The Scottish Conservatives take these issues extremely seriously.”
The party set up a support service in 2011 so people who had concerns could raise them directly and in confidence to a specially trained fellow member of staff – not the party whip.
But Ms Davidson said: “In the light of this weekend’s allegations, I have asked for those procedures to be reviewed so we can be certain that everyone who works for us feels reassured.
“We cannot be complacent. Our politics will be deeply diminished if young people are deterred from getting involved because of fear of harassment.
“Collectively, politics needs to get its house in order and make it clear that we do not accept the abuse of power in any way, shape or form.”