The NSW Government has lost its last-ditch effort to have a man face one trial over the murders of three Aboriginal children in the early 1990s, near Bowraville on the mid-north coast.

Key points: A man who can't be named was previously aquitted of murdering two of the victims

A man who can't be named was previously aquitted of murdering two of the victims The NSW Government was attempting to have him retried for two murders, and tried for a third suspected murder

The NSW Government was attempting to have him retried for two murders, and tried for a third suspected murder The three-judge High Court panel found there was no reason to doubt a previous decision rejecting the request

The NSW Attorney-General asked the High Court for leave to appeal against a 2018 ruling, that a man can't face a single trial over the deaths of four-year-old Evelyn Greenup and 16-year-olds Clinton Speedy-Duroux and Colleen Walker.

At previous trials, the man — who can't be named — was acquitted of murdering Clinton Speedy-Duroux and Evelyn Greenup.

The Attorney-General wanted him retried because of new evidence about the death of Colleen Walker, whose body has never been found.

A three-judge panel in the High Court has refused the request and found there was no reason to doubt the 2018 decision of the Criminal Court of Appeal (CCA).

Elijah Duroux, a relative of Clinton Speedy-Duroux reacted angrily outside court. ( ABC News: Kathleen Calderwood )

Family members in the packed public gallery said they were devastated by the decision, which also prompted angry reactions outside court.

"You have to have money in this place if you want justice," one man yelled outside.

Dolly Jerome, aunt of Clinton Speedy-Duroux, painted her hands with ochre and angrily painted the windows of the Law Courts building in Sydney with handprints.

"We are stuck in a 29-year rut of injustice," she yelled.

"We are owed, you owe us this justice, how dare you all!

"All we've done is appeal to the criminal system to get a murderer [prosecuted] for our three children — and somehow for 29 years, somehow, some way that's been evading us."

When the State Government lost its case in the CCA last September, the court found there was not enough fresh and compelling evidence to justify overturning the two acquittals and ordering a single trial for three murder charges.

Attorney-General Mark Speakman said the development represented "yet another blow" to the families who had fought for justice over three decades.

"I am sorry for the further trauma and grief today's decision will bring," he said in a statement.

Colleen Walker's body was never found, although a coroner ruled her dead. ( AAP: Supplied )

"Despite today's disappointing result, I believe that the retrial application was in the public interest."

Mr Speakman said there had been "failings" in the criminal justice system's initial response to the suspected murders and he hoped they would never be repeated.

"I am sorry that those failings continue to deny the children, and their families, the justice that they deserve."

The State Government would consider options following the decision, Mr Speakman added.