A cross-party group of MSPs has called on Scotland’s Deputy First Minister to formally extend the inquiry into whether Nicola Sturgeon breached the ministerial code.

They want John Swinney to widen the remit of the independent inquiry to include claims by Alex Salmond that the First Minister broke the code by allegedly misleading parliament over when she knew of sexual harassment claims against him.

Mr Salmond has also called for the investigation to be widened.

Ms Sturgeon initially told Holyrood she first heard of complaints of sexual misconduct against her predecessor when they met at her home on April 2 2018.

It later emerged she had an informal meeting with Mr Salmond’s chief of staff, Geoff Aberdein, in her Holyrood office four days earlier.

The SNP leader told a Scottish Parliament committee examining the Scottish Government’s botched handling of sexual harassment allegations against Mr Salmond she “forgot” about the encounter.

A spokesman for Ms Sturgeon said she denies Mr Salmond’s claims and stands by her previous comments on the issue.

Now, four members of the committee – Labour’s Jackie Baillie, Liberal Democrat Alex Cole-Hamilton and Conservatives Margaret Mitchell and Murdo Fraser – have written to Mr Swinney calling for him to formally extend the remit of independent inquiry into whether or not the First Minister breached the ministerial code.

They have also written to James Hamilton QC, who is conducting the inquiry, asking him to clarify if the inquiry will be expanded as requested.

Both letters state: “If corroborated, Mr Salmond’s evidence could prove that the First Minister knowingly misled Parliament both orally and in writing on several occasions about when she first knew that the government was investigating complaints against the former first minister and of her actions around the same.

“Equally, Mr Salmond may be fabricating his assertions in an effort to damage Ms Sturgeon. In any case these two versions of events cannot both be true and we believe it to be of paramount importance to the national interest that the facts of the matter are established.”

The letters say widening the investigation to include examination of whether Ms Sturgeon broke the section of the code dealing with knowingly misleading parliament is “vital”.

The MSPs tell Mr Swinney: “When asked previously, both yourself and the First Minister have repeatedly suggested that James Hamilton QC is at liberty to expand the remit of his inquiry should the evidence require it.

“However, we understand that as he engaged in a quasi-judicial process, he cannot indulge in mission creep and that the remit may only be formally expanded by an official directive from your government.”

A Scottish Government spokeswoman said: “The Deputy First Minister already confirmed to Parliament in November, in response to a parliamentary question from one of the authors of this letter, that the James Hamilton inquiry could look at any aspect of a potential breach of the ministerial code. We will not prejudge that process.

“The First Minister stands by her written evidence to the Parliament and looks forward to answering questions when she appears later this month.”

Mr Salmond said evidence he submitted to Mr Hamilton has also been given to the committee.

He added: “It is a matter for Mr Hamilton and committee members what they do with my evidence but I stand by the contents of the document and I am prepared to do so under oath in front of the committee.”