SACRAMENTO, Calif. — Gov. Jerry Brown ordered new DNA tests Monday that a condemned inmate says could clear him in a 35-year-old murder case that has drawn national attention.

Brown ordered new testing on four pieces of evidence that Kevin Cooper and his attorneys say will show he was framed for the 1983 Chino Hills hatchet and knife killings of four people. The items that will be tested are a tan T-shirt and orange towel found near the scene and the hatchet handle and sheath. Brown also appointed a retired Los Angeles County Superior Court judge to serve as a special master overseeing the case.

Cooper was convicted of killing Doug and Peggy Ryen, their 10-year-old daughter Jessica and 11-year-old neighbor Christopher Hughes in 1985. Prosecutors say Cooper's claims of innocence have been disproven multiple times, including by prior DNA testing, but Cooper and his attorney argue evidence against him was planted.

"I take no position as to Mr. Cooper's guilt or innocence at this time, but colorable factual questions have been raised about whether advances in DNA technology warrant limited retesting of certain physical evidence in this case," Brown wrote in his executive order.

Protesters rally in downtown San Francisco on Feb. 3, 2004, to denounce the possible execution of Kevin Cooper at San Quentin State Penitentiary. MARCIO JOSE SANCHEZ / AP file

New York Times' columnist Nicholas Kristof, U.S. Senator Kamala Harris, state Treasurer John Chiang and reality television star Kim Kardashian are among people who called for Brown to order new DNA tests. Cooper had his execution stayed in 2004, which drew national attention at the time.

Brown issued his Christmas Eve order alongside 143 pardons and 131 commutations. They are expected to be his last clemency actions as governor, but he has until he leaves office Jan. 7 to act.

The purpose of the new testing, he wrote, is to determine whether another suspect's DNA or the DNA of any other identifiable suspect is on the items. If the tests reveal no new DNA or DNA that cannot be traced to a person, "this matter should be closed," Brown wrote.

Two previous tests showed Cooper, 60, was the killer, argued San Bernardino County District Attorney Mike Ramos. He previously said the tests proved Cooper was in the Ryen's home, smoked cigarettes in the Ryen's stolen station wagon, and that Cooper's blood and the blood of at least one victim was on a T-shirt found by the side of a road leading away from the murders.

Jonathan Richman, at left, was among a group of anti-death penalty advocates attending a rally in downtown San Francisco, Tuesday, Feb. 3, 2004, ahead of Kevin Cooper's scheduled Feb. 10 execution. The execution was halted. AP

Cooper's attorney, Norman Hile, said his client's blood was planted on the T-shirt, and that more sensitive DNA testing would show who wore it. He contends that investigators also planted other evidence to frame his client, a young black man who escaped from a nearby prison east of Los Angeles two days before the murders.

Other evidence points to the killers being white or Hispanic, Cooper's supporters say.

A San Diego judge in 2011 blocked Cooper's request for a third round of DNA testing.

Cooper's scheduled execution in 2004 was stayed when a federal appellate court in San Francisco called for further review of the scientific evidence, but his appeals have been rejected by both the California and U.S. supreme courts. Former Gov. Arnold Schwarzenegger twice denied Cooper's clemency petitions.

California hasn't executed anyone since 2006.