Former First Minister Mr Salmond had been the subject of an inquiry by civil servants allegations of sexual misconduct were made against him, but a judicial review deemed that probe to be unlawful. He was cleared of 13 charges of sexual assault, including attempted rape, at the High Court in Edinburgh in March Ms Sturgeon then referred herself to his standards panel after it was claimed she had broken the strict code by not immediately declaring meetings she had held with her predecessor to discuss the misconduct claims.

James Hamilton, a former director of public prosecutions in Ireland, is currently looking at whether Ms Sturgeon breached standards of conduct.

Earlier this year, a remit set out by Deputy First Minister John Swinney said Ms Sturgeon’s role, if any, in the investigation into Mr Salmond would be fully scrutinised.

But in a letter earlier this month to Mr Hamilton – the adviser leading the inquiry into the First Minister – Mr Salmond has called for that remit to be widened.

He has asked if “equal status” will be given to investigating if Ms Sturgeon misled the Scottish Parliament.

The former First Minister has also asked if she failed to act on legal advice, and if civil servants did not give truthful information to Parliament.

Mr Salmond said the current remit could be a “straw man to knock down”.

He wrote in his letter to Mr Hamilton: “What I wish to know is whether matters which, by contrast, are specified in the ministerial code such as the primary responsibility of not misleading Parliament (contrary to 1.3 (c) of the code), such as the failure to act on legal advice suggesting the Government was at risk of behaving unlawfully (contrary to 2.30 of the code), and such as the ministerial failure to ensure civil servants gave truthful information to Parliament (contrary to 1.3 (e) of the code), will have at least equal status in your deliberations or are you confined to the political remit which you have been set?”

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The new push has been triggered by a meeting Ms Sturgeon had with Mr Salmond’s former chief of staff Geoff Aberdein on March 29, 2018, where she was informed of allegations against Scotland’s former First Minister.

Ms Sturgeon has been accused of misleading the Scottish Parliament by failing to disclose the details of her meeting with Mr Aberdein.

The ministerial code states: “Ministers who knowingly mislead the parliament will be expected to offer their resignation to the first minister.”

SNP leader Ms Sturgeon has told Parliament she did not know of the allegations until four days later when she was told by Mr Salmond himself during a meeting at her home.

She said she had forgotten the contents of her meeting with Mr Aberdein, adding it was her later meeting with Mr Salmond which was “seared on her memory”.

Mr Cole-Hamilton has said Ms Sturgeon should resign f the First Minister is found to have misled Parliament.