A deceased baby was cremated in Australia despite the parents wanting a burial after being incorrectly identified by a hospital staff.

Two babies — one stillborn and one miscarried — were mixed-up at Sydney's Royal North Shore Hospital last year because a blanket obscured an ID tag.

The incident follows a deadly newborn "laughing gas" mix-up at another Sydney hospital.

New South Wales Health Minister Jillian Skinner apologised for the incident.

"I'm devastated for them and I'm really sorry that such an incident occurred," she told a budget estimates committee.

A spokesman from the opposition Labor Party said Ms Skinner should be sacked to restore public confidence in the healthcare system.

However, Premier Mike Baird has stood by the embattled health minister in the wake of the hospital incidents.

"Jillian Skinner continues to do a good job in very difficult circumstances," Mr Baird said.