Federal Employment and Workplace Relations Minister Bill Shorten said that the government was calling a meeting with Telstra, unions, and other stakeholders on Monday to discuss issues arising after the discovery of asbestos at several locations during works for the rollout of the national broadband network.
"Asbestos is a giant scourge in this country. We can't afford to be complacent," Mr Shorten told reporters in Melbourne.
Unions have called for a fund to be set up, similar to one established for James Hardy workers, and Mr Shorten said that this would be discussed on Monday.
"I have some sympathy for that position, and we will talk about it further on Monday," he said.
Establishing a register for anyone that may have been exposed, and conducting an audit and removal of asbestos in pits involved in the NBN rollout would also be discussed, Mr Shorten said.
The government would also seek a commitment from Telstra that they would not walk away from any claims made by workers who may have been exposed to asbestos, he said.
"We're calling all the stakeholders together on Monday to make sure the voices of everyone that is concerned are not swept under the carpet," he said.
Telstra has stopped work preparing pipes and pits to be used for the NBN rollout, and deployed 200 specialists to manage cases of breaches in asbestos management by the telco and its contractors.
The telco giant launched an audit of contractors this week after finding several cases of "non-compliant asbestos management and removal".
Investigators from the workplace safety agency Comcare are investigating the work, health, and safety systems of Telstra and its contractors.
The Office of Asbestos Safety had also been tasked with coordinating a national response to the incidents.
Federal Health Minister Tanya Plibersek said she doubted that the asbestos risks linked to the NBN rollout could develop into a James Hardie-style situation.
Ms Plibersek acknowledged that some residents had reported being too scared to go home after families were evacuated from a Penrith street in western Sydney as a precaution following the reports of asbestos found in pits owned by Telstra.
However, environmental officers and Telstra were in the process of conducting checks to ensure that there was no risk of asbestos exposure, she said.
"We know that many people are worried about asbestos, and I think it's quite right that people are cautious," Ms Plibersek told reporters in Sydney on Friday.
"I think it's very important that people are careful, but there needs to be some balance as well."