The father of Shirley McKie has launched an appeal for cash to help fight for an inquiry into her case.
Ms McKie was cleared of leaving her print at a murder scene and given £750,000 compensation. On Wednesday, MSPs voted against revisiting the case.
Iain McKie appealed for £100,000 and said the credibility of fingerprint services had been "shot to pieces".
In parliament on Thursday, the Scottish Executive again rejected SNP pressure to conduct a public inquiry.
Ms McKie, from Troon, in Ayrshire, was cleared of lying on oath in 1999 after insisting that a fingerprint found at the scene of the murder of a Kilmarnock woman was not hers.
Pressure for a public inquiry has increased since the former detective was awarded compensation.
Mr McKie said he hoped to raise £50,000 to £100,000 for a "fighting fund" to bring a judicial review into the decision not to hold a public inquiry.
Launching an appeal for money, he said: "We've had hundreds of people from the media and from the public saying: 'Look we will support you in this'.
"So as of today, with our lawyers, we have decided that we are first of all going to seek a judicial review of the government's decision not to have an inquiry.
"Secondly, if that is not successful, we are going to look at a private prosecution.
Mr McConnell said the case had been acted on
"To do that we need cash."
The appeal has been backed by Dr Jim Swire, who lost his 24-year-old daughter Flora when a bomb exploded on board the Pan Am 103 flight over Lockerbie in 1988.
Dr Swire, who also watched First Minister's Questions, said: "I do believe that these two cases between them reflect crucially on the international reputation of Scotland's criminal justice system.
"I think that between the two cases the reputation across the world of our country and its criminal system in particular will depend upon how these cases are sorted out."
First Minister Jack McConnell told MSPs action had been taken after independent scrutiny and it was time to move forward.
However, SNP Holyrood leader Nicola Sturgeon insisted confidence in the justice system had been damaged.
At First Minister's Questions, Ms Sturgeon accepted that reforms had taken place at the Scottish Criminal Record Office, but said the integrity of the justice system was on the line.
She said: "We cannot know if those reforms will sort out what went wrong in the Shirley McKie case because we don't know what went wrong in the Shirley McKie case."
She went on to challenge Mr McConnell: "Isn't it time the first minister took his head out of the sand and took some decisive action to restore confidence in the Scottish justice system?"
Mr McConnell accused Ms Sturgeon of trying to undermine the will of the parliament by raising the issue following Wednesday's vote against further investigation into the case.
He told MSPs: "At no time at First Minister's Questions has Ms Sturgeon questioned the recommendations that were made by the then independent reports into the fingerprint service and the implementation of those recommendations since then."
He added: "The action that was taken was based on independent reports from independent investigations.
"That action has all been implemented and as a result of that I believe we can all move forward."
First Minister's Questions was being held in the parliament's temporary home at The Hub in Edinburgh.
MSPs have had to move while investigations continue into why a strut in the Holyrood chamber swung loose from its mounting.