Auckland Cranes director Tony Gibson said staff had been in contact with the man's family.
"Our thoughts are with the deceased and his family at this time and we have support here for our staff."
"Our common goal is to understand what happened and make sure this type of tragedy never happens again."
Gibson said the man was not an employee of Auckland Cranes but was contracted to work there.
Worksafe was investigating the death and said the incident was similar to one weeks ago in Te Puke where a man died at the Te Puke Sawmill.
Kiln supervisor Darel Barton, 49, died on March 28 from injuries he received when he was crushed between a loaded and a timber stack.
He was also a father of two.
Ruth Cook, of Worksafe, said it was understood the man killed in this morning's incident was crushed between moving and stationary plant (machine).
"This is the second incident of this nature in less than a month after a worker was fatally injured in Te Puke on 28 March," she said.
"WorkSafe is saddened to hear about another workplace fatality and the devastating effect that this incident will have on family, friends, and others in the business."
Vehicles at work continue to be a major cause of harm in New Zealand workplaces; 73 per cent of all work-related fatalities involve a vehicle or moving plant.
"If we are to see a reduction in harm, businesses must address this risk and put safe systems in place to ensure that both the driver and those working around the vehicle are kept safe," Cook said.
Police confirmed the man in the Wiri incident died at the scene.
