An Australian hospital is investigating after staff accidentally terminated a healthy fetus instead of its twin with heart defects, a month before a full-term pregnancy.

The incident at Melbourne's Royal Women's Hospital happened after the mother, who was 32 weeks into her pregnancy, had asked to have the unhealthy twin terminated, on her doctors' advice.

Once the mistake was discovered, the woman underwent an emergency caesarean section to terminate the unhealthy fetus, Sydney-based newspaper the Australian reported.

The hospital issued a statement stating that "a distressing clinical accident occured" and apologizing "for the loss suffered by the woman and her family."

State Health Minister David Davis said the hospital would conduct an independent investigation and that other government bodies may look into the matter.

He also suggested that the family at the centre of the mix-up could receive compensation.

"There's no question that this is an incident that everyone would have preferred had not occurred," Davis said, according to the Australian.

State Premier Ted Baillieu said the investigation would be as thorough as possible.

"I don't think it's appropriate for anybody to draw any conclusions other than this is a horrible tragedy," he said.

The woman's family issued a brief statement asking for privacy "at what has been a very difficult time for us," the BBC reported.