The Howard coalition government was aware that 12 years ago, there was an asbestos problem in Telstra's pits and ducts, federal Labor has said.
"The previous government knew all about it, and did nothing about it," Cabinet Minister Craig Emerson told Sky News on Tuesday.
Telstra has been accused of cutting corners when handing over infrastructure to the National Broadband Network (NBN) builder NBN Co, after contractors and communities raised fears that they had been exposed to the deadly material.
The Gillard government has been under pressure from the Coalition to explain when and how much it knew about the asbestos problem at Telstra.
Fairfax Media has said that the giant telco wanted to create an independent body to accelerate compensation, and sought approval from the Department of Workplace Relations in 2001.
However, the department, then under the ministerial leadership of opposition leader Tony Abbott, rejected the plan.
"He's the guy now complaining," Dr Emerson said.
"This is nothing more than a way of attacking the National Broadband Network by the Coalition."
Independent Senator Nick Xenophon called for an independent inquiry by the auditor general.
"This is a AU$40 billion project. How could this risk not have been managed better?" he said to reporters in Canberra.
Liberal Senator Simon Birmingham said the government had failed to show that it was capable of managing a major project.
Telstra had done what Prime Minister Julia Gillard and her communications minister could not, he said.
"Telstra is taking responsibility for getting things right at their end," Birmingham said. "The government needs to take responsibility and acknowledge the fact ... that there are indeed contractors for NBN who have mishandled asbestos."
Labor Senator Doug Cameron insisted that the government had reacted quickly and efficiently.
"It's absolutely essential that workers ... carry out their functions in as safe manner and the public is protected," he said.
Opposition regional communications spokesman Luke Hartsuyker said Communications Minister Stephen Conroy has questions to answer.
"Has undue pressure placed by the government on contractors caused the round of shoddy workmanship that is leaving us in this position?" he asked reporters.