Mark Lundy's defence lawyers say the fight to clear his name will continue despite him running out of options.

The latest hammer blow to their cause was delivered by the Supreme Court in Wellington on Friday, which rejected Lundy's appeal against his convictions for murdering wife Christine and 7-year-old daughter Amber in their Palmerston North home in August 2000.

"This is not the end of the road in Mr Lundy's fight to establish he has suffered a miscarriage of justice," say Lundy's lawyers Jonathan Eaton, QC, and Julie-Anne Kincade, QC, in a statement issued "on behalf of Mark Lundy".

Lundy has twice been convicted of the double murder, but the Supreme Court's decision not to grant him a third trial is probably the end of the line for the case in the court system.

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KEVIN STENT/STUFF Mark Lundy, pictured at his retrial, could take his case to the Criminal Cases Review Commission when it's established in 2020.

The only other avenues for Lundy to pursue are a pardon from the Crown through the royal prerogative of mercy, or taking the case to the Criminal Cases Review Commission when it's established in mid-2020.

The lawyers' statement says the commission won't face the restraints of the appeals process through the Court of Appeal and Supreme Court.

Lundy was again found guilty of the killings at a 2015 retrial, but his lawyers unsuccessfully argued for a third trial because scientific evidence subsequently ruled inadmissible by the Court of Appeal was heard by the jury.

It related to testing of central nervous system tissue found on one of Lundy's shirts, which also had traces of Christine's DNA.

At both the retrial and his original 2002 trial the Crown called what has been described as "novel" scientific evidence about the tissue.

SUPPLIED Mark Lundy has twice been convicted of killing his wife Christine and daughter Amber.

The statement says Lundy's supporters, including forensic experts from around the world, will continue to monitor international developments in that area and "will not give up the fight on behalf of Mr Lundy".

"History tells us that it is the passage of time that often provides the opportunity to demonstrate the weaknesses and dangers in relying on what is otherwise said to be novel but reliable scientific opinion."

Lundy and his legal team and supporters are disappointed with the Supreme Court's decision.

"The prosecution of Mark Lundy has been something of a testing ground for new or novel science never previously advanced in any court of law," the statement says.

"It is frustrating and very disappointing that Mark Lundy never had the opportunity to have his guilt or innocence determined by a jury who where not exposed to bad science – scientific opinion that a jury should not have heard."

Meanwhile, the Ministry of Justice has so far paid Lundy's defence team $64,634 in legal aid funding for the Supreme Court appeal, on top of $184,961 for taking the case to the Court of Appeal. Legal aid payouts include expert witness expenses and other costs.

The case has been costly down the years. Lundys lawyers at the retrial, London-based Kiwi David Hislop, QC, Ross Burns and Kincade had a legal aid bill of about $1.8m.

Crown Law paid lead prosecutor Philip Morgan, QC, about $210,000 for his role in the case, while fellow prosecutor Ben Vanderkolk was paid from the Palmerston North Crown solicitor's annual funding.

The two police investigations into the killings, Operation Winter and, for the retrial, Operation Spring, cost about $1.3m and $1.8m, respectively.

Lundy is eligible for parole in 2022.