The First Minister is being investigated around whether she breached the ministerial code around her handling of the Scottish Government’s botched harassment complaints procedure following two complaints against Mr Salmond.
Last week, in a submission to Mr Hamilton’s inquiry, the former first minister accused Ms Sturgeon of repeatedly breaking the ministerial code around meetings between him, his former chief of staff Geoff Aberdein, and the First Minister.
A cross-party letter from the Scottish Conservatives, Scottish Labour and the Scottish Liberal Democrats called for an urgent expansion of Mr Hamilton’s investigation by the deputy first minister John Swinney.
During First Minister’s Questions, Oliver Mundell, the Scottish Conservative MSP, asked Ms Sturgeon whether she would explicitly expand the investigation.
He said: “If the First Minister has nothing to hide, why won’t she explicitly expand the ministerial code investigation to cover all of the accusations that have been made against her?
"There is a big difference between saying that there are no limits on what James Hamilton can look at and explicitly asking him to examine specific possible breaches.”
In response, the First Minister said Mr Hamilton had written to the government and confirmed he did not see his inquiry as being constrained.
Ms Sturgeon said: “The Deputy First Minister has actually notified me this morning that Mr Hamilton has actually written to him confirming that in his views, all of the allegations – incidentally all of the allegations I completely refute about breaching the ministerial code – are covered within the scope of his existing remit.
"I said previously that I wanted him to go wherever he thought it appropriate to go and as I understand he has now confirmed that he feels there is no limitation on his ability to that.
"I hope the member will accept that and people will allow due processes to take their course rather than making their minds up before we even get to that.”
Any minister found to have breached the ministerial code by misleading parliament, something Ms Sturgeon is accused of having done, is expected to offer their resignation.