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Alfonso Salazar, 56, had been hospitalized since April 21. He was being housed at the Florence prison, located about 60 miles southeast of Phoenix.
Dale Baich, a federal public defender whose office represented him in an appeal, called the prison's medical care "poor" and said it is the "subject of ongoing litigation."
Salazar was sentenced to death in 1988 after he, along with another man, were convicted of murdering 83-year-old Tucson resident, Sara Kaplan two years earlier. She was found beaten and strangled by a telephone cord, according to Phoenix's KJZZ radio station.
They entered her home by prying open metal security bars from a window, the station added.
He's the first death row inmate in Arizona to die of coronavirus complications, and the third inmate in the state to die from the virus. At least seven other death row prisoners have tested positive for the coronavirus, Baich said.
One of the ill inmates said he and the others are being isolated in a dirty, cockroach-infested building.
The Florence facility accounts for 35 of the 50 coronavirus cases in state prisons.
The Associated Press contributed to this report