The union made the call after a worker was taken to hospital with serious injuries following an incident on the project on Monday, 06 March.
Unite regional officer John Clark said the organisation has had "ongoing concerns" over health and safety on the AWPR scheme, but too often "bosses aren't listening".
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"Our first thoughts are with the worker who has been injured and with his friends and family. No worker should be put in a position where they don't return safely home from their shift," he said.
"We have had ongoing concerns over health and safety on the AWPR project but too often, bosses aren't listening. We need proper dialogue between the contractors and their workers and union reps, and when things go wrong we need openness and transparency so that we can put them right as soon as possible.
"Safety should be a top priority on every construction project – and especially on a flagship public project like this one. Our officers and workplace reps will continue to monitor working conditions on the project, and will be making sure that workers' voices are heard in any investigation."
(LM/JP)
