The leaders of three Scottish political parties have signed a motion calling on ministers to address concerns over the Shirley McKie fingerprint case.
Shirley McKie received compensation over the case
Tory Annabel Goldie and the Greens' Robin Harper have supported the move by SNP Holyrood leader Nicola Sturgeon.
Her motion, which will be debated by MSPs, follows a call by retired High Court judge Lord McCluskey for more transparency in the justice system.
The Scottish Executive said there was no need for a public inquiry.
Ms McKie was cleared of lying on oath in 1999 after insisting that she had not left a fingerprint at a murder scene nine years ago.
Pressure for a public inquiry has increased since the former detective was awarded £750,000 in compensation.
The motion, which will be debated in SNP time at Holyrood on Thursday, said issues have arisen in the case which imply that justice has not been seen to be done.
It also agrees with Lord McCluskey that the issues involved are not party political "but go to the heart of public trust in the criminal justice system".
The motion "calls on the Scottish Executive to consider how the concerns expressed by Lord McCluskey should be addressed".
Ms Sturgeon said: "The purpose of the motion is not to back the executive into a corner but to debate the issues and examine ways of moving forward.
"The fact that this motion has unprecedented cross-party support highlights the seriousness of this case.
"This is an opportunity for Labour and Lib Dem ministers to reconsider their position over the Shirley McKie case and realise that justice must be seen to be done."
Ms Goldie said: "It was important for all parties who are trying to deal with this matter responsibly to unite and secure a sensible outcome.
"If Labour and the Lib Dems had their way, these questions would have gone unanswered.
"It is our duty to make them face up to their responsibilities as a government."
Green MSP Patrick Harvie said: "This whole affair has caused deep damage to public confidence in our justice system."
But an executive spokeswoman said: "We do not consider that yet another inquiry would shed any new light on an incident which occurred nine years ago.
"There have already been two inquiries into SCRO and the recommendations of each have now been implemented.
"The changes which have been made to the fingerprint service in Scotland over the last few years have been substantial. The staff there are providing a sound, professional service in the delivery of justice."