The Tasmanian Premier, Paul Lennon, says he wants a full independent inquiry, but not a public inquiry.
The union says it wants the terms of reference for the inquiry to be broadened.
This would include whether the design and operating standards of the mine contributed to the rockfall that killed miner Larry Knight and trapped Brant Webb and Todd Russell for a fortnight.
The union's secretary Bill Shorten says he is not interested in assigning blame, but wants to ensure no one else has to go through the same trauma.
Mr Shorten said there had been seven fatalities in underground mining in Tasmania, and about 170 mining deaths over the last 10 years nationwide.
"We are sick of reading about and attending work sites and dealing with the families (and wives) of miners who have been tragically and catastrophically turned into widows," he said.