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A baby has died and another is in critical condition after both were administered "laughing gas" instead of oxygen at a hospital in Sydney.

The error was the result of a faulty gas line which was dispensing nitrous oxide at Bankstown-Lidcombe Hospital.

A doctor discovered the problem after the baby died unexpectedly.

New South Wales Health Minister Jillian Skinner said she felt "profound sorrow" at the "tragic mistake" and ordered an investigation.

"I deeply regret these families have suffered through such a devastating error. NSW Health will do all it can to support them," she said.

Sonya Ghanem, the mother of the newborn who died, : "I said, 'I want to see him.' Just looking at him, shaking. 'My son, wake up,' I would tell him. 'Wake up, wake up. What did they do to you?' "

Ms Skinner said the gas lines were checked and certified by the gas company, BOC Ltd and the hospital. The legal counsel for New South Wales has demanded an explanation from BOC Ltd.

In a statement, the company said: "We deeply regret that these families are suffering pain and sorrow."

BOC Ltd is carrying out an internal inquiry.

Ms Skinner has ordered all medical gas lines to be checked. "Mothers can feel confident that we have checked every operating theatre, every [resuscitation] bay where babies are treated and there are no other examples of this, " she said.

Media in Australia criticised Ms Skinner for attending a performance awards ceremony as news of the gas incident emerged.

The opposition party has called for her resignation, but Ms Skinner says she will not stand down.