Communications, Electrical and Plumbing Union (CEPU) official David Mier has said that up to 85 percent of National Broadband Network (NBN) contractors working in pits containing asbestos have not completed the required safety training.
Workplace safety watchdog Comcare has confirmed that it is investigating a range of issues related to Telstra pits.
Mier said that up to 60 workers on 13 sites he had visited in Tasmania had not received asbestos awareness training.
"The pit and pipe work should be stopped where people haven't done asbestos awareness courses," he told AAP.
"If you are part of the general public, you would want to know that people who are removing asbestos pits out the front of your house have been trained to do so."
Mier accused NBN Co contractor Visionstream of cost cutting, and said the lack of training means that sites are being left dangerously exposed.
"Kids wagging school or little kids just playing, they just jump in there thinking it's a sandpit," he said.
A spokesperson for Comcare said the government body is already taking action at some sites.
"Comcare is currently investigating a range of regionalised issues with Telstra pits and contracting arrangements, including the ones in Hobart," a statement said.
"Comcare is intervening on specific sites, and are working with NBN and Telstra to enhance the current systems, including the asbestos awareness training area."
NBN Co said it is awaiting details so it can confirm whether the problems are occurring at its sites.
"We've asked the union for specifics, so we can investigate these claims thoroughly," a spokesperson said.
"We've yet to receive that information."
The company said it requires all construction staff and contractors to complete an approved safety course that includes asbestos awareness.
"Worker safety and public health are our top priorities," the spokesperson said.
Mier said he will deliver a report to the companies involved, as well as federal Communications Minister Stephen Conroy on Thursday.
Areas of Tasmania were chosen to be among the first in Australia to be connected to the multibillion-dollar broadband network.