Tasmanian independent Jacqui Lambie has challenged the government to deregister the construction union, just like Bob Hawke did with the Builders Labourers Federation.

But Employment Minister Eric Abetz says that was only possible because Mr Hawke led a responsible Labor government supported by a responsible coalition opposition.

Senator Lambie used parliament’s question time on Tuesday to accuse the Construction, Forestry, Mining and Energy Union of ignoring the law despite court-imposed penalties.

The CFMEU leadership was involved in a wide range of serious criminal activities and associated with “outlaw bikie gangs, killers and underworld figures”.

Why hasn’t the government which had been in office for two years deregistered the CFMEU just as the Hawke government did in 1986, Senator Lambie asked.

The BLF was deregistered at the federal level and in most states in 1986 following a royal commission into union corruption.

Its federal secretary Norm Gallagher was jailed.

Building workers are now represented by the CFMEU.

Senator Abetz said it was a toss of a coin to choose between the BLF and CFMEU.

“The situation was that in the Hawke era you had a responsible Labor leadership supported by a responsible opposition – there was unanimous support in the parliament,” he said.

In that time a “proud union movement and a proud Labor leader were willing to call corruption as corruption, thuggery as thuggery”.

“I would be very interested to see if there would be support for that,” Senator Abetz said.