Sixty four of Pembrokeshire's 70 schools contain some asbestos - but Pembrokeshire County Council will not curently say which schools they are.
The figure was revealed following a question from county councillor David Bryan, prompted by the recent closure of Cwmcarn High School, in Caerphilly, due to asbestos.
Pembrokeshire County Council's cabinet member for education, Huw George, told councillors at the meeting of full council last Thursday that the Health and Safety Executive recommended that asbestos products should be left in place, providing they were in good condition, and should be subsequently managed.
He said that the schools' premises managers had a duty to ensure that all staff and visitors to the school were given information regarding the asbestos management procedure.
He added that the council had robust systems in place for the management and regulation of asbestos containing material in all Pembrokeshire schools.
Cllr George said he was disinclined to name the schools containing asbestos.
"I'm concerned about scaremongering", he said.
"Im reluctant to go public on which schools. Levels of asbestos are different from school to school".
Cllr George said he would go back to the director of education and social services and discuss whether the schools should be named.