New DNA evidence could help exonerate a man on death row in the US state of Texas for the murder of his girlfriend and her two adult sons, his lawyers claimed Thursday.

Hank Skinner, 51, has been on death row for 20 years over the 1993 triple murder. He has always denied the charges against him.

A private Virginia laboratory on Thursday published the results of tests conducted on four hairs found in the hand of the slain woman, Twila Busby -- and three of them show a family link with the three victims.

The fourth belongs to Skinner -- a result the lawyers called "unremarkable," given that the accused lived in Busby's house.

"The doubts about Mr. Skinner's guilt are far too weighty to allow his execution to proceed," said his attorneys, Robert Owen and Douglas Robinson.

A spokesman for the Texas attorney general's office, however, quickly dismissed the claims, saying the findings still showed Skinner's guilt.

For Skinner's lawyers, the three hairs show a link to the victims via their maternal side, supporting the theory that Busby's late uncle Robert Donnell carried out the crimes.

Donnell "stalked Ms. Busby and frightened her with crude sexual advances at a New Year's Eve party less than an hour before she was murdered," the lawyers said in a filing to a Texas court, accompanied by the lab results.

A first series of DNA tests found traces of Skinner's DNA on the murder weapon as well as that of an unidentified third person, leading Texas prosecutors to say the case against him was strengthened.

Skinner told AFP in an interview in May that he was confident he would eventually be exonerated. He calls a last-minute reprieve from the US Supreme Court in 2010 a "miracle."

He has never denied being at the scene of the crime, but says he had taken a combination of vodka and pills that would have made it impossible for him to carry out the violent crime.

Skinner's lawyers said "parties will confer to determine whether technology exists that would allow additional DNA testing that could produce potentially relevant results."

The Texas attorney general's office, meanwhile, decried Skinner's "continual delay tactics."

"The latest test results continue to show the link between Hank Skinner and his guilt in the murder of Twila Busby," a spokesman for the office, Jerry Strickland, told AFP by email.

"Hank Skinner's case is exactly the reason why this office supported a new law requiring DNA evidence be tested before trial instead of continuing to delay justice."