Nicola Sturgeon has been urged to curb the SNP’s influence on the Holyrood inquiry into the Alex Salmond affair in order to maintain public trust.

The SNP will automatically be offered the chair of the special committee being set up to examine the case, as it is the largest party at the Scottish Parliament.

Scottish Labour said the SNP should step aside and give the powerful role to someone from another party to avoid any impression of bias.

Labour also urged Ms Sturgeon to ensure internal SNP documents and emails were surrendered to the inquiry if MSPs requested them.

Read more: MSP probe into Salmond and Sturgeon may be paused to avoid police clash

Ms Sturgeon is under fire for having three meetings and two phone calls with Mr Salmond while her officials were investigating two sexual misconduct allegations against him.

Ms Sturgeon has told parliament the meetings were “party business”, although she also said she did not tell her husband, SNP chief executive Peter Murrell, what was said in them.

Holyrood is establishing a committee to examine Ms Sturgeon’s conduct and the reasons behind the spectacular collapse of the government’s misconduct probe.

Mr Salmond last week won a court challenge over how the probe was run, forcing ministers to admit it had been flawed and unfair, leaving taxpayers with a £500,000 legal bill.

At First Minister’s Questions, interim Tory leader Jackson Carlaw asked Ms Sturgeon “what on earth she was doing” meeting Mr Salmond while he was under investigation.

He quoted back her own words to her from 2007, when she said then Scottish Labour leader Wendy Alexander could not hide behind police and watchdog inquiries over her donations without answering the obvious questions of “who knew what, when and how”.

However Ms Sturgeon refused to answer about her own role and that of her chief of staff, Liz Lloyd, telling Mr Carlaw he should wait for the inquiries he himself had asked for.

She said: “I will answer any question to the fullest extent possible and that my Government will co-operate fully with all and any inquiries.

“Other members in the chamber now need to recognise that, having asked for these investigations, they are obliged to respect them.

After Mr Carlaw persisted, she said he was making “party political points”.

Mr Carlaw said that the “tawdry business and her handling of it in the past seven days” had fundamentally undermined trust in her Government.

The FM said the real tawdry thing was Scotland being dragged out of the EU by Brexit.

She also revealed the government’s own inquiry into its botched investigation would be “externally led”, with ministerial work on it delegated to her deputy John Swinney.

Labour leader Richard Leonard said the Holyrood inquiry was “the right thing to do in order to rebuild trust and confidence in a system that has been badly dented”.

He said: “So will the First Minister’s party do the right thing? Will it step aside and ensure that an MSP from another party chairs the inquiry?”

Ms Sturgeon dodged the question, saying it was not for her to decide who sat on the inquiry.

When Mr Leonard asked if “all internal SNP correspondence” would be given to the committee, Ms Sturgeon said: “The inquiries will be able to request whatever material they want, and I undertake today that we will provide whatever material they request.

“That is the definition of full, thorough and open inquiries. It will not be for me to decide what material the parliamentary inquiry, when it gets under way, wants to request. My commitment is that the Government and I will cooperate fully with it, which is, I think, appropriate.”

Mr Leonard also said the committee should meet in public, not be subject to any time limit

He said later: “Let’s not forget that two women have been badly failed by the system, and they are entitled to answers, which is why the parliamentary inquiry must be as thorough as possible. This is an unprecedented situation and Nicola Sturgeon must agree that this inquiry will be chaired by an opposition MSP. Nicola Sturgeon should do the right thing.”

Mr Carlaw said the FM could not keeping ducking questions she demanded others answer.

He said: “Nicola Sturgeon has been caught out - when the boot was on the other foot she said opponents couldn’t hide behind inquiries, now she’s in the spotlight she’s dashing for the long grass. For her to attack those asking legitimate questions about this scandal is beneath the office of First Minister.

“On the conduct of both the Scottish Government internal inquiry and the Scottish Parliamentary inquiry, these inquiries need to be thorough and transparent – and be seen to be so. The SNP must show they are committed to that so we get to the bottom of this affair.”