The education minister admitted that he is not satisfied with current levels of asbestos management in schools on 27 November 2012.
"I do not feel sufficiently assured at this stage that local authorities are discharging their statutory duties to manage asbestos and have sufficient plans in place," Leighton Andrews AM said.
The minister had called on all local authorities to produce their asbestos management plans and contingency plans in the event of school closures after
Cwmcarn High School
in Caerphilly was shut in October after asbestos was found there.
He stressed however that he would not be calling for the removal of asbestos in all schools.
"The Health and Safety Executive has always maintained that the best approach for asbestos in sound condition and not likely to be damaged is to leave it well alone, protect it and manage it to prevent damage and exposure to asbestos," he said.
During his short debate, Monmouth AM Nick Ramsay called on the Welsh government to reveal the information on asbestos levels in schools rather than concealing parents' right.
Growing concern about asbestos levels in schools has led to calls for routine testing for airborne fibres in classrooms in Wales.