A newborn baby has died after it was given nitrous oxide instead of oxygen in hospital.

A second baby is in a critical condition after it was also given the gas - known as laughing gas - at Bankstown-Lidcombe Hospital in Sydney.

Both children were treated with a dispenser of nitrous oxide that had been wrongly installed as oxygen in the hospital's neonatal resuscitation unit.

New South Wales health minister Jillian Skinner has apologised after the problem was discovered when the second baby died and a paediatrician raised concerns.

She said: "I am profoundly sorry for the families of a newborn who died and another newborn who was severely affected.

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

"The oxygen outlet in one of the hospital's theatres was incorrectly installed and certified by BOC Ltd in July 2015."

The grieving families - whose children were born in June and July this year - were told about the mistake at the weekend.

Eight operating theatres at the hospital have since been checked but the one affected remains closed, while staff have confirmed that no baby born since July 2015 has been treated with the wrong gas.

Nitrous oxide and oxygen are both odourless and colourless, but BOC's company website suggests its oxygen gas tanks are black, while those filled with nitrous oxide are light blue.

South Western Sydney Local Health District has launched a probe to investigate if hospital staff followed rules that may have uncovered the installation error last year.

Other health facilities in the region have been asked to check their gas outlets and review protocols for ensuring they are properly installed.