Education Secretary John Swinney faces a no-confidence motion at Holyrood later over the exams controversy but the vote is expected to be defeated.
The Scottish Conservatives, Scottish Labour and the Lib Dems want him to resign after thousands of teacher estimates were downgraded.
But the Scottish Greens have said they will not support the motion, following a government U-turn.
They said they were satisfied now that teacher estimates have been reinstated.
This year’s grades were based on teacher assessments because exams were cancelled due to the coronavirus pandemic.
When the results were published last week 125,000 of those estimates were downgraded by the Scottish Qualifications Authority, which said it wanted to ensure the results were comparable with previous years.
But there were claims this system unfairly penalised pupils at schools which had historically not performed so well.
On Tuesday, after an outcry and protests by students, Mr Swinney said he would direct the SQA to reissue grades “based solely on teacher or lecturer judgement”.
At First Minister’s Questions on Wednesday Scottish Labour leader Richard Leonard said the government had been repeatedly warned the system would not work - and John Swinney had seen the results five days before they were published
He said: “He could have saved all those people from all that anguish, he could have saved you, first minister, from having to make a grovelling apology but he did not. Why isn’t his neck on the line?”
Ruth Davidson, leading the Conservative party at Holyrood, claimed John Swinney had been a “common denominator” in a series of failures in education.
“The first minister’s loyalty to a colleague may be commendable but her real loyalty should be to the parents and pupils of Scotland. They deserve new leadership in education and John Swinney cannot deliver it.”
Scottish Lib Dem leader Willie Rennie has described Mr Swinney as “part of the problem, not the solution”.
Nicola Sturgeon, however, has stood by the education secretary, accusing opposition parties of caring more about political advantage than seeking the best outcomes for young people during the most “horrendously difficult set of circumstances”.
She told MSPs: “We will continue to lead the country through this as best we can, and we will not shy away from saying when we get things wrong and taking the action we need to do to put them right.
“I do think that’s what people prefer to the traditional approach to politics we have in more normal times.”
Scottish Greens education spokesman Ross Greer told BBC Scotland his party had demanded the problem be fixed as the price of its support in the no-confidence vote.
“We used our leverage to resolve the situation, that has now happened - we will not support the vote of no-confidence,” he told The Nine.
“All along what the Greens wanted was a solution for young people, and they are far more interested in getting their grades fixed than in the political theatrics of whether or not John Swinney goes.”
A motion of no-confidence must be debated if tabled by 25 or more MSPs but it is an expression of parliament’s opinion, and not legally binding.