Scottish Labour has voted against plans for a Holyrood investigation into the botched handling of an internal inquiry into sexual assault claims against Alex Salmond after the Scottish National party insisted on chairing it.

Labour and the Conservatives had urged the SNP to allow another party to chair the special committee, which had all-party support until it emerged a former SNP minister would be appointed to lead it.

All five Holyrood parties agreed to the inquiry after the Scottish government conceded in court last month it had seriously mishandled an internal investigation into allegations of sexual assault made against Salmond by two women. He strongly denies any wrongdoing.

Scottish Labour called for the Holyrood inquiry and asked Nicola Sturgeon, the leader of the SNP and the first minister, to allow another party to lead it.

Her spokesman insisted decisions on convening committees was a matter for parliament.

On this occasion, under Holyrood’s procedures, the SNP was due to chair the next committee to be established. Any party in that position is able to relinquish the convenorship if it wants to but on this occasion Sturgeon opted not to do so.

The SNP has appointed four ex-ministers to the eight-strong committee – Linda Fabiani, Angela Constance, Maureen Watt and Alasdair Allan, all of whom served in government while Salmond was first minister.

Graeme Dey, the Scottish government’s parliament business minister, told the chamber that it would nominate Fabiani as the committee’s convenor. Since Fabiani is currently a deputy presiding officer of the Scottish parliament, he said that should reassure MSPs that the inquiry would be conducted in a non-partisan way.

Dey said the process for setting up the committee and appointing its convenor had been unanimously supported by all five parties. SNP sources said that included the Tories and Labour’s business manager at Holyrood, Neil Findlay.

In a brief debate on Wednesday before Holyrood voted by 92 to 19 in favour of establishing the committee, Findlay said the inquiry would also be investigating Sturgeon’s actions and those of her close advisers.

“It is essential for the standing of this parliament that we get this right,” he said. “[Can] this parliament be trusted to do things openly and transparently in the national interest? This is a big test for us all. It is vital that any committee is not compromised before its work begins and there is no perception of inbuilt bias.”

Annie Wells, for the Tories, who voted in favour of the committee along with the SNP, Scottish Greens and Liberal Democrats, said they still wanted the SNP to voluntarily relinquish control of it.

“There’s a clear public interest in ensuring that this committee is both impartial and seen to be impartial,” Wells told Dey. “There is no getting around it: that will be more difficult in these very particular circumstances.”

Salmond launched a legal challenge to the government’s processes in the civil courts last year after it emerged Leslie Evans, the permanent secretary of the Scottish government, had completed her investigation and passed a dossier to Police Scotland.

In January, she admitted it had unlawfully allowed a senior civil servant who had had previous contact with two women who made allegations against Salmond to lead the internal investigation. That gave it the appearance of bias, Evans conceded.

Salmond, who denies all the allegations, was arrested and charged in late January with 14 counts involving two of attempted rape, nine charges of sexual assault, two of indecent assault and one breach of the peace.

The Holyrood inquiry is not expected to begin until after the court process is concluded.