With the opposition on Monday leading a parliamentary attack on the government over its alleged lack of urgency in tackling asbestos discovered in Telstra junction pits being handed over to the NBN, Fairfax Media has learnt the giant telco wanted to create an independent body to accelerate compensation and sought approval from the Department of Workplace Relations more than a decade ago.

However the department, then under the ministerial leadership of Mr Abbott, rejected the plan, which it is understood enjoyed the support of unions at the time.

The emergence of Telstra's previous attempt to get on the front foot on the issue came as Telstra agreed on Monday to take ''ultimate responsibility'' to deal with asbestos used in its infrastructure.

Amid the developments, opposition communications spokesman Malcolm Turnbull tried to tag NBN Co as inept and portray the current Labor government as having dragged its feet on the issue.

Workplace Relations Minister Bill Shorten said it was regrettable politics was being played on asbestos.

''This issue should be off-bounds. If they've got a view about how Telstra should do business safely, the door's open, but the fact of the matter is it's the Labor side that has always pushed asbestos awareness, asbestos legislation, the asbestos agency, and compensation at Hardies,'' Mr Shorten said.

During a crisis meeting in Canberra on Monday, Telstra agreed to set aside compensation funds and take part in an independent taskforce to oversee any future claims by victims

Mr Shorten said the meeting did not agree to establish a new fund for asbestos victims but Telstra chief executive David Thodey had assured the government that provisions had been made.

The taskforce, to be chaired by asbestos expert Geoff Farey, will ensure compensation is paid where necessary.

The taskforce will include senior Telstra executives, Asbestos Diseases Foundation president Barry Robson, the Chief Medical Officer and Commonwealth and state regulators.

On Monday, urgent legislation that would facilitate a new national asbestos register also passed the lower house. If it clears the Senate, Australia would become the first nation to create a national body to prevent more people being exposed to deadly asbestos fibres.

The Asbestos Safety and Eradication Agency, an independent body, would focus beyond workplace health and safety to include public health issues.

In question time, Prime Minister Julia Gillard accused Mr Abbott of exploiting the issue for political gain. ''I suppose we should not really be surprised given that this is the same person who insulted Bernie Banton on his death bed,'' she said.

Mr Abbott had said of the asbestos campaigner and sufferer: ''I know Bernie is very sick, but just because a person is sick doesn't necessarily mean that he is pure of heart in all things.''

Residents have been forced to move from their homes in Penrith, western Sydney, after subcontracted construction workers digging up Telstra equipment to make way for the NBN exposed asbestos in the lining of existing copper wires.