Mr. Reed was convicted of the 1996 murder of Stacey Stites in Bastrop, Texas. Ms. Stites, 19, was strangled, and her body was dumped alongside a rural road. Prosecutors said she had also been raped, and Mr. Reed was arrested based mostly on DNA tests.

He maintained that he and Ms. Stites had been having an affair, which would explain how his DNA was recovered from her body.

Mr. Reed’s lawyers have argued previously that the state’s forensic investigators made critical errors regarding the timeline of the killing, which some investigators later admitted in affidavits.

Most recently, at least three people have come forward with new testimony regarding Ms. Stites’s fiancé, Jimmy Fennell. Mr. Fennell is a former police officer who was released from prison in 2018; he pleaded guilty in 2008 to kidnapping a woman he had encountered while on duty. The woman said he had also raped her.

A man who served time in prison with Mr. Fennell said in a sworn affidavit last month that he had heard Mr. Fennell confess to killing Ms. Stites because she had cheated on him with a black man. Mr. Reed is black.

Mr. Fennell’s lawyer, Robert M. Phillips, said that Mr. Fennell denies killing Ms. Stites.

It was unclear whether Friday’s ruling would lead to a resolution of one of the most contentious issues in the case: Mr. Reed’s lawyers have pushed for the murder weapon — Ms. Stites’s belt — to be tested for DNA evidence, which has yet to happen.

Mr. MacRae said he expected that an evidentiary hearing would take place in another four to six months, in which the new witnesses would testify and other evidence would be examined in court. He said it was possible that Mr. Reed’s defense team would also subpoena Mr. Fennell.