The group wants the material removed after studying estimates which suggest the deadly material was present in more than 75% of schools.
More than 140 teachers have died from the rare asbestos-related cancer mesothelioma in the past 10 years.
Education chiefs say it is unacceptable for schools to ignore guidance but that undamaged asbestos should be left.
Last year, the Department for Education (DfE) revealed that its "best estimate" was that more than three-quarters of schools contain asbestos.
The Parliamentary Group on Occupational Safety and Health's chairman, Jim Sheridan, said: "This is a national scandal.
"Urgent action is needed to prevent more pupils, teachers and other staff being exposed to this deadly killer dust.
"We need both far greater awareness of the risks that this material poses and a programme for its phased removal."
The group's other recommendations include annually updating parents, teachers and staff about asbestos in their schools, and reinstating inspections into asbestos management.
A DfE spokesman said: "HSE's expert advice is based on the best current evidence.
"It is absolutely clear that if asbestos is not disturbed or damaged, then it is safer to leave it in situ, with strong systems in place to contain and monitor it."