Green, 47, was killed Friday when a shaft at the privately owned Roa mine, 800m below ground, collapsed.
Nine other men were working in the shaft at the time of the collapse and managed to escape without injury, the New Zealand Herald reported.
Engineering Union secretary Andrew Little said investigations will be undertaken by the mine’s owner, safety inspectors and possibly the police.
Little said the union’s key concern is to see that the investigations are thorough and any wrongdoing or failure is addressed.
Green was a father of five, a former Kiwi rugby league player and popular Greymouth identity, the New Zealand Herald said.
At least 20 men work at the mine, which operates 24 hours a day, mine rescue officials said. They said it was not immediately clear what had caused the tunnel to collapse.
The Roa mine is owned and operated by Roa Mining Company, a joint venture between Francis Mining Company and Coaltrac AG.