The kiln has been repeatedly shut down due to health and safety breaches and concerns about the gas emissions.
Last week the kiln at the Whirinaki site malfunctioned and emitted toxic fumes that hospitalised four workers, one worker even became unconscious.
Ms Delahunty said no one should be forced to work in a dangerous workplace while WorkSafe waits around for the mill bosses to do their own investigation.
"When workers are striking out of fear their workplace is too dangerous, the Government needs to step in to ensure WorkSafe is doing its job - actually making workplaces safe.
"I've heard from people in Hawke's Bay that the toxic kiln has been a problem since it was installed in 2014, and it's been a real struggle to get anyone from WorkSafe or the regional council to take the problem seriously. If the kiln isn't safe, it shouldn't be operating."
WorkSafe has been engaged with the company and the union on issues surrounding the kiln since September 2014, a spokeswoman said.
"Up until the February 23 incident we have been unable to identify through our inquiries/investigations that any serious harm has been caused to either workers or residents in close proximity to the plant."
An investigation is now under way into that incident.
WorkSafe placed one prohibition notice on the company prohibiting it from operating the kiln at full commercial capacity. This notice allowed the kiln to be operated to test its integrity and once it had completed three full cycles without incident, the prohibition notice was lifted.
"Based on the information we have obtained up to the February 23 incident, it was, and remains, our firm view that the kiln operations are a matter for the company and the union to manage, and there was to that point no evidence of serious harm which would have justified WorkSafe's regulatory intervention."
WorkSafe continues to be informed of progress.
First Union organiser Mike McNab said this week that workers had made their concerns known to the company and to WorkSafe on countless occasions.
"This is not the first time a serious health and safety breach has happened and workers fear it won't be the last.
"They need to have some control over not working in unsafe conditions, the health and safety strike gives them this."
Although the kiln is currently under lockdown pending an investigation, union members have lost all confidence that the kiln can be operated safely, Mr McNab said.
The health and safety strike action will only be lifted when members are confident that their workplace is safe and vote to lift it.