FORMER first minister Henry McLeish has called for Holyrood's powers to be strengthened to give MSPs the same level of legal protection as MPs in statements they make in the chamber.

McLeish's intervention comes after David Davis used "parliamentary privilege" in the Commons last night to make public material he said was handed to him by “an anonymous whistleblower” which suggested there was a "criminal conspiracy" against Alex Salmond among senior figures in the SNP close to Nicola Sturgeon.

Parliamentary privilege allows Davis to speak freely without fear of prosecution. MSPs speaking in Holyrood do not have the same levels of legal protection.

Davis said Holyrood had been limited in its ability to hold the Scottish Government to account over the flawed investigation and called for MSPs to have the same level of parliamentary privilege as MPs.

For instance, proceedings in Holyrood, unlike those at Westminster, are subject to contempt of court law.

READ MORE: SNP MP asks if police will speak to David Davis over Alex Salmond whistleblower leaks

Speaking to The National, McLeish argued the row between Sturgeon and Salmond had underlined a need to enhance MSPs' privilege powers and that this change should get under way now.

"Twenty-two years on from the creation of Holyrood, the Parliament has matured, we've have gained a lot of experience, and the spat between Sturgeon and Salmond has re-enforced the need for more significant powers [relating to absolute privilege] for our parliament as we move forward," he said.

"I can say no reason why Scottish parliamentarians should not have the same powers as parliamentarians at Westminster. In this day and age the Parliament needs all the powers it can to hold governments to account and I think it would be a welcome freedom used sparingly. This matter should be for early discussion for the Lord Advocate, the law officers and Westminster.

"The time is right now for this idea to move forward."

McLeish noted there may be some resistance among some in Westminster for such a move as some he believed regard Holyrood as "an inferior parliament".

The former first minister went on to say the matter would have to be examined with regard to the Scotland Act 1998, which established the Scottish Parliament and which he helped to steer through the Commons as a Labour minister.

"We need to move on and this would be one aspect of moves to strength the Scottish Parliament which I have been asking for," he added.

Speaking in the Commons during an adjournment debate on Tuesday evening, Davis said he believed issues relating to the Scottish Parliament's committee inquiry into how the Scottish Government mishandled complaints against the former SNP "are unquestionably something that should properly be dealt with in Holyrood".

WATCH: Nicola Sturgeon rejects David Davis's claims about Alex Salmond evidence

However, he added that "Holyrood has great difficulties exposing what went on" and argued those difficulties "can be traced back to the Scotland Act 1998, in which the British Government of the day and this House decided to devolve power to the Scottish Parliament but failed to do it properly".

Davis cited the more limited privileges MSPs were given compared to MPs over what they can say without fear of prosecution.

The former Brexit secretary said: "It is because of these failings that I have brought this debate today. We need to reinforce the ability of the Scottish Parliament to hold its own Government to account. I am here to strengthen the Scottish Parliament, not to bury it."

MSPs on the committee looking into the Scottish Government Handling of Harassment Complaints are preparing to publish their report into the matter.

The probe was established after a successful judicial review by Salmond resulted in the Scottish Government's investigation being ruled unlawful and "tainted by apparent bias", with a £512,250 payout being awarded to him for legal fees in 2019.

The First Minister spent eight hours being questioned by the committee on March 3.

Her deputy John Swinney told BBC Radio Scotland's Good Morning Scotland programme today that the inquiry should be left to come to its conclusions.

He said: "The First Minister spent eight hours of the harassment committee giving comprehensive answers to every question that was put to her and she stands by all of that information.

"We've set up the process of inquiry, I think we should let it take its course and come to the conclusions that we need to, as I've said we will do, in connection with the reports that arise out of these events."

Commenting on Sturgeon's appearance at the committee, he added: "The First Minister gave an open and candid account of the involvement that she's had and her recollections of this process and obviously we await the outcome of the different inquiries that are looking at these issues."

The First Minister has denied there was a conspiracy against Salmond.

Section 41 of the Scotland Act provides that for the purposes of the law of defamation any statement made in "proceedings of the Parliament" and the publication under the authority of the Parliament of any statement is absolutely privileged. This means that any such statement cannot form the basis of an action for defamation.

The section is intended to ensure that members are free to debate and the Parliament to report on matters of public interest without fear of an action for defamation being raised. Although it provides absolute protection in that context, it does not shield members from the operation of the law in relation to other matters, for example incitement to racial hatred.