Telstra is hiring an extra 200 safety specialists to inspect all asbestos-related work at sites where the National Broadband Network (NBN) is to be rolled out.

Several sites in New South Wales, Victoria and Western Australia have been shut down and some residents have been moved from their homes over concerns about asbestos exposure.

Telstra's chief operations officer Brendon Riley says an audit of all the underground pits will be finished by tomorrow.

As part of the NBN rollout, Telstra is required to repair and modernise the telecommunications pits around the country.

While Telstra has strict guidelines concerning asbestos management and removal, it has outsourced the job in Penrith to sub-contractors Service Stream.

There have been similar breaches at NBN sites in Ballarat, Victoria and Mandura, a suburb of Perth, Western Australia. But Mr Riley says the asbestos at those two sites has already been removed.

Mr Riley says Telstra takes full responsibility for the clean-up.

"We are going to be taking responsibility for all field supervision of asbestos-related remediation. We're going to take on responsibility for all of the training in terms of asbestos handling for ourselves and our contractors... we already do it for ourselves," he said.

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Federal workplace safety regulators have shut down work on parts of the NBN while they investigate the asbestos safety breaches.

"One situation like this is one too many and I think we saw a lot of strong feedback from the community, particularly in Penrith," Mr Riley said.

"Asbestos is a serious issue, not just for us but as a national issue, and we thought it was time to take some steps and that's what we announced today."

The Communications, Electrical and Plumbing Union wants Telstra to set up a James Hardie-type fund for workers who suffer from asbestos-related diseases in the future.

NSW Assistant Secretary Shane Murphy says Telstra is to blame for subcontracting the work to companies who failed to properly train their workers to handle the toxic material.

"Some years ago, when Telstra used to manage this work and do these work functions in-house, its workers were put through proper safety and training courses in relation to handling asbestos," he said.

"What's now happening is - and for some time - Telstra has outsourced those responsibilities to the contractors, who then outsource it to other contractors down the food chain.

"And again, it's as simple as we've got the processes and policies in place, but there's actually no real training going on other than people signing off and saying 'I've worked with asbestos or been trained in its safe handling'."