The Scottish Conservatives are pushing for the vote over John Swinney’s handling of the Alex Salmond case.
The Scottish Conservatives say they will push for a vote of no confidence in John Swinney “on Tuesday or Wednesday”.
Leader Douglas Ross said he also wanted to see a similar vote against Nicola Sturgeon unless further legal advice in the Alex Salmond case was released.
The Scottish government published legal advice related to its court battle with Mr Salmond last week.
Mr Swinney had previously argued such advice should remain confidential.
But the deputy first minister then said he had taken the “exceptional step” to rebut “false allegations” made about the Scottish government’s legal advice over the judicial review brought by Mr Salmond.
The move came after all opposition parties indicated they would back a motion of no confidence in Mr Swinney last week if he did not comply, with the SNP government facing defeat.
But Mr Ross said that threat had only resulted in a “partial” release of “vital evidence”, adding that the deputy first minister’s position had now become “untenable”.
The Scottish Conservatives said they planned to hold a vote of no confidence in Mr Swinney on Tuesday or Wednesday, with a similar vote in Ms Sturgeon “shortly afterwards”.
Holyrood’s other opposition parties could back the move if further documents are not released, they said.
A spokesperson for the Scottish government said all formal written advice from external counsel during the judicial review had now been disclosed.
But speaking on BBC Scotland’s Sunday Show, Mr Ross said the Holyrood inquiry still needed to fill in the gaps in what happened at key meetings about the case involving the Scottish government.
“The [no confidence] vote is not off the table because after an eight-hour evidence session – where the first minister said she’d answered all the questions which clearly she hadn’t – the Scottish government issued more evidence that we’d been calling for.
“Why was that evidence not made available before the first minister came in front of the committee?”
Mr Ross said there was still a “blank” to fill regarding a meeting between the first minister and her permanent secretary on the case.
“There was no minutes taken? I don’t think anyone believes that’s the case, so we are still pushing the deputy first minister… this week on that vote of no confidence, to release all the evidence that the committee needs to get to the truth of this matter.”
The legal advice published this week shows that Scottish government lawyers had “reservations” about its court battle with the former first minister more than two months before it conceded the case.
The judicial review was examining whether the government’s handling of harassment complaints against Mr Salmond was legal.
The review found against the Scottish government, resulting in them having to pay Mr Salmond’s legal fees of more than £500,000.
The Scottish government said it had taken “unprecedented steps” to provide the committee with the information it had requested, releasing a “huge amount of documentation”.
A spokesman added: “We have now disclosed all of the formal written advice notes received from external counsel during the judicial review, as well as a number of other relevant previously legally privileged documents.
“As the deputy first minister has set out, these documents, taken in their entirety, utterly disprove the conspiracy theory that the Scottish government delayed the concession of the judicial review or ignored advice from counsel.
“The information in the documents is consistent with information already shared with the committee in evidence.”
The Scottish Liberal Democrat leader Willie Rennie said they would “seriously consider” backing a vote of no confidence in Mr Swinney unless the documents demanded by parliament were produced.
The Greens said their position remained that the government must provide all the evidence required by the committee.
Labour are also understood to have concerns over the withholding of some documents.