An Australian woman who was convicted of killing her four children 18 years ago has petitioned the New South Wales governor for a pardon.

Kathleen Folbigg, 53, was convicted on three charges of murder and one of manslaughter in 2003 and was sentenced to 30 years in prison.

But dozens of scientists have backed her claims that her children died from natural causes and claim she could be the victim of a tragic miscarriage of justice.

Folbigg has petitioned for a pardon "based on significant positive evidence of natural causes of death" for all four of her children.

The petition, lodged in March, has been signed by 90 scientists, medical professionals and two Nobel laureates.

Shortly after the petition, three judges threw out her challenge to a 2019 decision by Justice Reginald Blanch to uphold her convictions.

Her appeal had been based on new scientific evidence including the children's genome sequencing.

After her latest court defeat, Folbigg said in a statement written from prison through her friend Tracy Chapman that the verdict and the petition raised "valuable questions about how we got here".

"Many international eyes are now on this case and there're many more Australians rightly asking why Kath's still in prison after 18 years when there's mounting scientific evidence relating to her innocence," Ms Chapman wrote.

The signatories of the petition disagree with the latest court ruling.

Australian Academy of Science president John Shine accused the three appeals court judges of adopting the same "incorrect conclusions about the genetic evidence" as Mr Blanch.

"It is deeply concerning that there is not a mechanism to appropriately weigh up all medical and scientific evidence in a case of this nature," Mr Shine said.

"There is now an alternative explanation for the death of the Folbigg children that does not rely on circumstantial evidence."

Folbigg's first child Caleb was born in 1989 and died 19 days later in what a court determined to be the lesser crime of manslaughter.

Her second child Patrick was eight months old when he died in 1991.

Two years later, Sarah died aged 10 months.

And in 1999, Folbigg's fourth child Laura died at 19 months.

Folbigg was the first on the scene of each tragedy and an autopsy found Laura had myocarditis - an inflammation of heart muscle that can be fatal.

Patrick suffered from epilepsy and his death had been attributed to an airway obstruction due to a seizure and an infection.

The other two deaths were recorded as sudden infant death syndrome.

Paediatric geneticist Jozef Gecz, who signed the pardon petition, acknowledged the evidence of natural causes was stronger in the girls' deaths than the boys.

But he said investigations were continuing into potential leads to genetic causes of the boys' deaths.

The criminal case against Folbigg relied on interpretations of entries she had made in diaries, one of which her estranged husband Craig Folbigg read and reported to the police.

Folbigg's case has parallels to Sally Clarke, the solicitor who was wrongly convicted of murdering her two baby sons in 1999.

Mrs Clarke, who served three years of a life sentence, was found guilty of smothering her 11-week-old child to death in 1996 and shaking her eight-week-old son to death in 1998.

The convictions against Mrs Clark were upheld on appeal in October 2000 but overturned in a second appeal in 2003.

It emerged during the second trial that Alan Williams, the prosecution forensic pathologist who examined both babies, had failed to disclose microbiological reports that suggested the second of her sons had died of natural causes.

The outcome led to Lord Goldsmith ordering a review of hundreds of other cases and two other women had their convictions overturned.

Mrs Clarke died in her home in 2007 from alcohol poisoning.