The society says Saskatchewan has shown leadership by being the first province in Canada to do so.
But the group says the province should go further and make the registry mandatory for all public buildings.
The registry is to include the legislature, court houses and equipment storage buildings.
But it will be voluntary for schools, hospitals and health region buildings.
The society says students, patients and staff deserve the same protection from asbestos, which can cause cancer if the fibres are inhaled.
Asbestos is typically found in building materials such as insulation. It is not considered harmful if undisturbed, but renovations or construction work stir up hazardous fibres.