An investigation is underway after it was confirmed that staff at an Australian hospital accidentally killed the wrong fetus during an abortion.

The abortion that went horribly wrong was initially designed to terminate one of two 32-week-old twins, who doctors say had a "heart defect", as BBC reports.

Sources say the Victorian mother chose to have an abortion after doctors explained that if born, the sick fetus had little chance of survival and would face a tough life of constant heart surgeries if it did survive.

In a statement the hospital said they "can confirm a distressing clinical accident occurred on Tuesday...We are conducting a full investigation and continue to offer the family and affected staff every support."

After learning that her healthy unborn had died, the mother went on to have an emergency caesarean in order to end the life of the sick twin.

Many have been left outraged, disturbed at the possibility that medical professionals could make such a fatal and careless mistake.

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Victorian State Premier Ted Baillieu urged the public to wait for the outcome of an investigation before weighing in. The BBC quoted him as saying: "I don't think it's appropriate for anybody to draw any conclusions other than this is a horrible tragedy.

"We'll make sure that the investigation is as thorough as it can be."

The family is said to be devastated and have requested privacy during what is undoubtedly a "difficult" time.

The state of Victoria passed legislation to decriminalize abortion in 2008.

Christianity is said to be the predominant faith amongst Victorians.