Souza, 31, is charged with fatally stabbing inmate Edward John Schaefer in the prison's reception center yard on July 26.
His arraignment on Friday and today were postponed so a defense attorney could be appointed, Marin County Deputy District Attorney A.J. Brady said.
The Marin County Public Defender's Office cannot represent Souza because it represented Schaefer during his court proceedings.
Schaefer was at San Quentin State Prison awaiting transfer to another facility to serve a 24-years-to-life term for second-degree murder and mayhem in connection with a DUI crash that killed a Novato girl and injured her father.
Schaefer, 44, of Novato, was stabbed in the neck and chest. He was taken to Marin General Hospital and died at 9:03 p.m. on July 26, the Marin County coroner's office said.
Souza is currently serving a 60-years-to-life sentence for first-degree murder of a homeless man, John Carl Riggins, 59, in the Willow Glen neighborhood of San Jose on Aug. 29, 2007, according to the California Department of Corrections and Rehabilitation.
The Marin County District Attorney's Office could seek the death penalty for Souza because he is charged with first-degree murder with special circumstances of having a prior murder conviction, Brady said.
Souza also is charged with assault with a deadly weapon by a prisoner serving a life term and with being an inmate in possession of a weapon, Brady said.
Schaefer was sentenced on July 13 in Marin County Superior Court to 24 years to life in prison for second-degree murder and mayhem.
Schaefer's Harley Davidson motorcycle struck 9-year-old Melody Osheroff and her father, Aaron Osheroff, of Novato in a crosswalk on May 27, 2009.
Melody died the next day at Oakland Children's Hospital and her father lost his right leg as a result of the collision.
Prosecutors estimated Schaefer's blood-alcohol level at the time of the crash was between 0.11 and 0.16 percent.
Souza has three prior prison commitments, Department of Corrections and rehabilitation spokeswoman Terry Thornton said.
He served an 18-month sentence in 1998 for grand theft in Santa Clara County, a 2-year term in 1999 for receiving stolen property, and a 4-year sentence in 2002 for threatening a prosecution witness with force and violence in Santa Clara County, Thornton said.
Souza began serving his life sentence in San Quentin State Prison for the San Jose murder on Jan. 12, Thornton said.