The blast occurred at the facility on East Moors Road on Wednesday, 18 November.
Emergency services were called to deal with a fire in the bar and rod mill in the basement of the plant at 10:30am.
One victim was treated at the scene and another four were taken to hospital.
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Two people have since been discharged.
Celsa Steel said it is now working with the HSE and police who are investigating the incident.
"Our thoughts and deepest sympathies are with those affected and their families, who have been informed," the firm said.
"Operations have been suspended and the fire services have confirmed that the Mill is safe. Safety is our paramount concern at all of our facilities and the wellbeing of our colleagues is our number one priority.We wish to thank the emergency services for their rapid response and support."
Supt Stephen Jones, of South Wales Police, said the focus was now on the recovery of bodies, supporting the families and finding out what caused the explosion.
(LM/CD)
