Alex Salmond has escalated his attacks on Nicola Sturgeon’s government by implying that the Scottish first minister’s accounts about a sexual harassment investigation into him have been misleading.

Salmond, Sturgeon’s predecessor as first minister, alleged on Monday that her chief of staff, Liz Lloyd, knew of harassment claims against him in early March, before he had been officially told by the Scottish government that he was under investigation.

His claims came the day after Sturgeon had referred herself to an independent ethics body, which investigates claims of ministerial misconduct in Scotland.

In a day of tit-for-tat accusation and counter-accusation between the pair, Sturgeon’s political spokesman accused her former mentor and close friend of conducting a smear campaign against her.

The Times published claims by Salmond’s aides on Monday morning that Lloyd knew of the investigation and she had contacted him on 6 March to warn him of that fact.

The Sun published a story which claimed Sturgeon also knew at that time, an allegation Salmond now appears to have retracted.

Sturgeon’s spokesman responded to the claims in an official statement: “This appears to be an attempt to smear the first minister. Suggestions by Mr Salmond’s ‘insiders’ that the first minister knew about the investigation before 2 April are not true. The suggestion put to Ms Sturgeon’s chief of staff by the Times, that she knew of complaints when she met someone who could be described as an intermediary for Alex Salmond on 6 March, is also not true.”

Opposition parties are to discuss on Tuesday whether to hold an independent Holyrood inquiry into the entire controversy, which could be launched after the independent commission on the ministerial code has issued its findings.

Sturgeon told the Scottish parliament and reporters last week she first learned that Leslie Evans, Scotland’s chief civil servant, had launched the investigationfrom Salmond in person when they met in secret at her home on 2 April.

Sturgeon is under fire for failing to alert the civil service to that meeting and a subsequent phone call with Salmond on 23 April until two months after the meeting and also for allowing herself to be lobbied by him five times.

The first minister told reporters on Thursday she had not been told in advance about the subject of that meeting. Her spokesman then told reporters that Lloyd was not aware of it, either.

Salmond retaliated against the smear accusations on Monday by releasing an official statement which repeated his allegations against Lloyd, claiming she initiated the contacts which led to the 2 April meeting.

“In the interests of accuracy it is the case that the first minister’s senior special adviser knew of the existence of complaints against Alex some time before the meeting of 2 April and that she initiated the first contact through an intermediary,” the statement said. “They then arranged the meeting which Alex asked for. Alex has no certainty as to the state of knowledge of the first minister before then.”

Salmond’s press release then referred to the possibility that Sturgeon may have broken the ministerial code.

If Salmond’s claims about Lloyd’s intervention are accurate, it remains unclear whether she was referring to the two cases under investigation by Evans.

Salmond robustly denies any wrongdoing, but it has been reported that a parallel police investigation into those two complaints has been expanded to include other alleged incidents.

The latest developments mark a new low in the relationship between Sturgeon and Salmond, once her close friend and mentor. They have not spoken in nearly six months.

The row also deepens a growing rift within the Scottish National party, which hoped to capitalise on the UK government’s disarray over Brexit this week by building up the case for a second Scottish independence referendum. Senior SNP figures say privately that the strategy has been comprehensively undermined by the feud.