The meeting in was also attended by Ms Sturgeon’s chief of Staff, Elizabeth Lloyd, but the First Minister has insisted that it was not government business.
Opposition parties have called on Ms Sturgeon to refer herself to the watchdog that investigates breaches of the Ministerial Code, claiming that she breached rules requiring government officials to be informed of meetings relating to public duties.
The First Minister says she was clear she could not intervene in the case on all the occasions she met Mr Salmond.
The Scottish Government conceded a legal action brought by Mr Salmond over its handling of the investigation, after it emerged a civil servant given responsibility to look into the claims had made previous contact with the two women involved.
The case has cost the taxpayer £500,000 and prompted calls for the resignation of Leslie Evans, the head of the civil service in Scotland.
Mr Salmond denies the allegations. He has said he wishes to take up his membership of the SNP, which he resigned to bring the legal action.
Jackson Carlaw, the interim Scottish Tory leader, said the First Minister’s explanation of the meetings “simply doesn’t stack up”.
Referring to the meeting as the “Saturday Summit” at Ms Sturgeon’s home, Mr Carlaw said: “She can’t claim she was ambushed by Mr Salmond. They’d already spoken three times at this point. So why did she hold this meeting?
“What did Mr Salmond tell Ms Sturgeon about the investigation? What involvement did she, or any of her aides, have at this time? Why did the First Minister follow it up with a phone call four days later? Were discussions held about ways to bury this whole sordid affair?
“Failure to answer these questions make a Holyrood inquiry inevitable.”
A Scottish Government spokesman said: “The First Minister has already set out her meetings and phone calls with Alex Salmond.
“Mr Salmond … raised his concerns about elements of the process and informed the First Minister he was proposing mediation and arbitration.
“As the First Minister told Parliament, she was clear to Mr Salmond that she had no role in the process and would not intervene.”