It came as Ms Sturgeon rejected claims by Scottish Greens co-leader Patrick Harvie that a “significant number of high-profile people within the SNP” had been allowed to get away with promoting transphobia.
Mr Harvie, who is also a government minister following a co-operation agreement between the SNP and the Greens, said transphobia had been allowed to “fester”.
Speaking to The Scotsman onboard the SNP’s campaign bus, Ms Sturgeon said this was “absolutely not” the case.
She said: "Patrick Harvie, when he's doing interviews as co-leader of the Scottish Green Party, is going to say things I disagree with, and that's one of them.
"I'm sure I'm going to say things when I'm doing interviews as leader of the SNP that he would disagree with.
"That's in the nature of being different political parties.
"So I don't agree with that, and I don't think it is right and I don't think it's justified."
The Scottish Government is seeking to reform the Gender Recognition Act to simplify the process for a trans person to legally change their gender.
Current rules require individuals to obtain a medical diagnosis and spend a minimum of two years living as their chosen gender.
Supporters say the move will streamline a process many find distressing, but critics have raised concerns self-identification will undermine women’s sex-based rights, such as access to women-only spaces.
Ms Slater sparked controversy last week after she said in an interview: “We wouldn’t put balance on the question of racism or antisemitism.
“But we allow this fictional notion of balance when it comes to anti-trans [views]. The whole thing is disgusting.”
Scottish Tory MSP Meghan Gallacher said the remarks arguably amounted to a breach of the ministerial code, and accused Ms Slater of equating “those who have legitimate concerns over the impact of this legislation on women’s rights and safety with racists”.
SNP MP Joanna Cherry QC tweeted: “Scotland deserves better than this.”
Asked if she agreed with Ms Slater’s comments, the First Minister said: "I don't agree with the characterisation of the comments, but I don't think Lorna said what she was, in some respects, characterised as having said.
"What she said was transphobia should be treated as negatively as racism and sexism.
"What she did not say was that anybody who takes a different view on the gender recognition legislation, anybody who has concerns about that or anybody who wants to have a civilised debate about that, should be treated in that way.
"So I agree with what she actually said. I don't agree with what some people characterise her as having said."
Senior SNP politicians, including Finance Secretary Kate Forbes, have previously expressed concerns about aspects of the GRA reform.
Asked if her party will allow a free vote on the issue in Holyrood, to avoid repercussions if MSPs go against the party whip, Ms Sturgeon said this would be decided by the SNP group.
But she added: "SNP MSPs were elected on a manifesto commitment around this just a year ago, and I think that's quite an important consideration."