The union has written to the Confederation of Paper Industries (CPI) expressing its concern over the number of deaths and serious injuries in the paper industry during the last few years.
Bud Hudspith, Unite health and safety adviser, said the union has called for a meeting with the CPI in June to discuss a strategy for improvement.
"We are expecting the CPI to respond positively," he said. "In the meantime, we will be gathering evidence of health and safety problems in the industry from our officers dealing with paper mills."
A statement addressed to all officers in Unite's Graphical, Paper and Media (GPM) sector has also been issued by both Unite and the CPI, with full cooperation from Arjowiggins, warning them to address the issues raised in the safety alert.
It includes critically reviewing existing risk assessments and safe operating procedures for all machine intervention, and checking that arrangements meet the required standards.
The action follows the death of 45-year old man at Arjowiggins' Ivybridge mill last month.
The man died after becoming trapped in a paper machine at Arjowiggins' Ivybridge fine paper mill in Devon on 28 April.
He had been attempting to remove broken paper from a drying cylinder.
Following the incident, all production at the site was stopped and representatives from the Health & Safety Executive (HSE), along with the police, visited the facility.
The HSE announced on the afternoon of 29 April that production activities could recommence, subject to agreed terms.
Its investigation into the exact circumstances surrounding the incident is still ongoing, with the full co-operation of the company.
Following the death, Unite's assistant general secretary Tony Burke claimed the tragedy was "another massive blow" to the papermaking industry.
Arjowiggins parent company Sequana declined to comment.