A spokesman for the Naval Service said that, to date, all 55 Naval Service personnel who had any potential contact with the substance had been screened.
A further 54 civilian workers employed by the Department of Defence have also been screened and just seven remain to be checked.
The LÉ Ciara and LÉ Orla still remain out of action due to the discovery of asbestos onboard some months ago.
An expert clean-up of both vessels got under way on May 28 and it is thought they will remain in dry dock for another few weeks until the operation is complete.
The alarm was raised after it was discovered that some asbestos was being broken up on board during routine maintenance and that it may also have been broken up in workshops at the Naval Service’s headquarters on Haulbowline Island.
Asbestos becomes dangerous if it is broken up, as dust can get into people’s lungs and cause serious illness or death.
It can take up to 40 years for the symptoms to appear. Both PDForra, which represents enlisted men in the Naval Service, and Siptu, which represents most of the civilian workers, have called for continued medical checks to be carried out on all personnel over the coming years.
The Naval Service spokesman said a fleet-wide survey will be carried out for asbestos and a contract will be signed with an expert company shortly.
Senior officers were caught off guard following the recent asbestos discoveries because in 2000 they had been told by consultants that all their vessels were asbestos-free.