Nicola Sturgeon says Alex Salmond may be angry with her because she refused to "collude" to make sexual misconduct allegations against him "go away".
Speaking to Sky News, the first minister also read out messages between the two after claims they had been withheld from an inquiry.
A source close to former first minister Mr Salmond denied he was angry.
They said he was however "astonished at the ever shifting sands" of Ms Sturgeon's story.
Mr Salmond's lawyer has previously suggested the Scottish government may be trying to "malign his reputation".
It comes after the Scottish government had to pay Mr Salmond more than £500,000 in legal costs after accepting that its own investigation into allegations of misconduct against him was unlawful.
Mr Salmond was acquitted of sexual assault charges after a trial at the High Court in Edinburgh in March.
Nicola Sturgeon has previously said that she has not spoken with her former friend and mentor since July 2018.
She has faced accusations that she has been less than forthcoming with the Holyrood inquiry set up to investigate her government's botched handling of the harassment allegations.
In an interview with Sophy Ridge On Sunday, Ms Sturgeon said: "I think the reason perhaps he [Mr Salmond] is angry with me - and he clearly is angry with me - is that I didn't cover it up, I didn't collude with him to make these allegations go away and perhaps that is at the root of why he is as annoyed as he appears to be."
Ms Sturgeon said much of the criticism she has taken over the issue was the "age-old" situation where "a man is accused of misconduct against women and often it's a woman that ends up sitting answering for them".
In response, Mr Salmond said: ''I have made no public comment since I was acquitted of all charges in the High Court in March and have made it clear that the first time I will comment is in front of the parliamentary committee.
"This committee was established to inquire into the conduct of the first minister, her special advisers and civil servants after her government's behaviour was found to be 'unlawful', 'unfair' and 'tainted by apparent bias' and at enormous cost to the public purse."
The committee's chair, SNP MSP Linda Fabiani, has said the inquiry had been "completely frustrated" by the lack of evidence being handed over.
She said the committee was still awaiting responses from the government, Mr Salmond and SNP chief executive Peter Murrell.
Ms Sturgeon has repeatedly rejected claims that she has withheld information from the inquiry.
She insisted that "every day I've tried to do the right thing and not cover it up".
However, a source close to Mr Salmond said: "Alex Salmond is not "angry" with the first minister; just astonished at the ever shifting sands of her story.
"Her claims of an attempted 'collusion' are not only untrue but unsupported by the written evidence and directly contradicted by her own previous parliamentary statements."
The source added: "The first minister claims to be entirely focussed on a health pandemic where people are still dying but is lashing out on television about matters which should properly be dealt with in front of the parliamentary committee established for that very purpose."
The first minister has faced accusations that she withheld some WhatsApp exchanges with Mr Salmond, but insisted they were "not a big revelation".
She acknowledged that the messages did make "an oblique reference" to claims of inappropriate conduct by Mr Salmond - despite saying she released all relevant evidence to the Holyrood investigation.
Challenged about the claims on the Sophy Ridge programme, Ms Sturgeon offered to read out the messages.
She said she was "setting up a conversation" to discuss an inquiry by Sky News in 2017 about Mr Salmond allegedly behaving inappropriately.
Ms Sturgeon said the messages were sent during the week of 5 November 2017, and Mr Salmond had not previously told her he was to start hosting a show on Kremlin-backed broadcaster Russia Today.
Asked about the undisclosed messages, Ms Sturgeon said: "Around about the time I spoke to [Mr Salmond] about the Sky News query, I sent him a message on 5 November saying, 'Hi, when you free to speak this morning?'. He replies saying '10am'.
"That's when I asked him, 'What is this Sky thing?'
"I go back to him later that day to say, 'Any developments?'
"The next day, I say, 'You free for a word?'
"So I was setting up a conversation that I have told the parliamentary inquiry about, it's hardly a big revelation.
"Later that week, incidentally, I messaged him to say, 'No wonder you didn't want to tell me'. That's just after I find out that he's agreed to host a regular show on Russia Today, and it reflects my incredulity at that decision.
"I think his response to me then makes an oblique reference to the Sky News query, so that may be what he's talking about."
Pressed as to why Mr Salmond could want these messages to be released to the parliamentary inquiry, Ms Sturgeon suggested the former first minister might want people to believe the allegations were "all a big conspiracy" to deflect from his conduct.