Mr Salmond, the former leader, alleges WhatsApp messages suggest Peter Murrell – the SNP’s chief executive and Ms Sturgeon’s husband – put the police under pressure to pursue sexual harassment allegations against him.
In March last year, he was acquitted of all charges of sexual assault and attempted rape, following a two-week jury trial.
Asked about the controversy, Ms Sturgeon vowed: “I did not mislead parliament. And that's what I will say all too clearly when I get the opportunity.”
The first minister was expected to give evidence to a Holyrood inquiry in the coming days, but said her appearance had been delayed by a “couple of weeks”.
On the Andrew Marr Programme, she was asked “what you knew and when you knew it about the allegations against Mr Salmond”.
But Ms Sturgeon insisted she would “never apologise for doing everything I can to make sure that complaints about sexual harassment were investigated”.
And she replied: “I appear to be simultaneously accused of colluding with Mr Salmond to somehow cover up the accusations of sexual harassment on the one hand – and then, on the other hand, of being part of some dastardly conspiracy to bring them down.”
Asked about her own spokesperson accusing her predecessor of spreading “conspiracy theories”, Ms Sturgeon said: “There are false conspiracy theories being spun about this.”
She added: “I will sit before that committee and I will set out my account of what happened, given the very difficult situation that I faced, and people can make their own judgments on that.”
Ms Sturgeon has insisted she first found out about a complaint against Mr Salmond on 2 April 2018 – and that she forgot about a meeting with his former aide four days earlier, which was not recorded.
“If the SNP win the Scottish election in a few months' time, on the proposition of giving the Scottish people that choice, then what democrat could rightly stand in the way of that?” she asked.
She ducked a question about whether she would hold an advisory “home-made Scottish referendum” if Mr Johnson – as expected – refuses to sanction an official poll.
“I want to have a legal referendum, that's what I'm going to seek the authority of the Scottish people for in May,” Ms Sturgeon said, “and, if they give me that authority, that's what I intend to do. That's democracy. It's not about what I want or about what Boris Johnson wants, it's about what the people of Scotland want – and the increasing evidence is that they want independence.”