Independent MSP Brian Monteith this week submitted a motion calling for the schools to be inspected as an "urgent priority". He responded after The TESS also revealed that some 300 Scottish schools had not seen a full inspection report since between 1983 and 1995.
"Following the Scottish Executive's original announcement in 2002 of a generational cycle of inspections, the revelation that there are 32 schools that have not had inspection reports since the 1980s is an embarrassment and a national scandal," he said.
"My intention is to see this issue raised in parliament so that action is taken and HM Inspectorate of Education comes to terms with this failure. I find it astounding that the inspectorate will not concede that there is even a backlog.
"The inspectorate has a duty to ensure that priority is given to schools that are long overdue a full inspection, especially when it's believed that some other schools have had two visits in that time."
HMIE started its "generational" programme of inspections in 2002, when it told parents to expect reports within seven-year cycles for primary schools and six for secondaries, meaning every school should have been inspected by 2009.
It reacted to last week's story by insisting that there was no backlog, and that it was confident of completing the cycle on time.