A call by the Communications Electrical and Plumbing Union (CEPU) to create a fund for workers affected by asbestos comes after Telstra confirmed on Wednesday that it had suspended a contractor and shut down a NBN construction site in Penrith because of asbestos contamination fears.
More sites have since been shut down by federal workplace safety regulators, News Limited reported.
CEPU NSW Assistant Secretary Shane Murphy said that Telstra must set up a register for all workers who have been exposed to asbestos while working on the network.
"The impacts of this mess will be felt decades into the future," he said.
"Telstra needs to take responsibility for the health impact on its own workers, as well as the broader community."
CEPU national NBN construction and project officer David Mier compared the NBN rollout to the government's botched pink batts insulation scheme.
"The federal government blames NBN Co, NBN Co blames Telstra, Telstra blames the subcontractors, and in the end nothing changes," he said.
"What we are currently seeing on the NBN project is serious pyramid subcontracting — the work just gets sublet and sublet and sublet — resulting in one of the biggest subcontracting scams around."
Australia Post has stopped delivering mail to the affected Penrith street because of asbestos fears.
James Hardie, which was formerly heavily involved in Australian asbestos mining and manufacture, in 2001 set up a medical research and compensation fund to meet its asbestos liabilities.
Telstra said it had established a hotline on 1800 067 225 for residents concerned about work in their area.
Prime Minister Julia Gillard said Communications Minister Stephen Conroy had spoken to Telstra chief executive David Thodey and "made it very clear that Telstra does need to act".
"I am in a position to be assured that Telstra is acting," Ms Gillard told reporters in Canberra. "I am concerned about asbestos generally. I am concerned about this."
Telstra is deploying 200 specialists to NBN sites around the country and maintaining a ban on all remediation work amid fears workers may have been exposed to asbestos.
Chief operations officer Brendon Riley says Telstra is "deeply concerned" by the situation and will take every precaution necessary to strengthen Telstra's asbestos management.
The team of field workers will directly inspect and supervise all asbestos related remediation work training, he said.
Update: Additional information from Telstra, the Prime Minister, and CEPU added.