Police released a vague description Friday morning of a possible suspect, who is described as a white male between the ages of 40 and 49 years old.
Sgt. Steve Martos said the "limited description" came from an interview with the Rev. Joseph Terra, who is hospitalized in critical condition with unspecified wounds.
There is a $1,000 reward for information leading to an arrest.
Police are still unsure if there was only one suspect involved or whether robbery was the motive in the attack at the Mother of Mercy Mission, Martos said.
A vehicle belonging to the Rev. Kenneth Walker, who died at a hospital late Wednesday, was found abandoned a few blocks from the church.
Police were investigating whether the suspect or suspects took the 2003 Mazda and left it behind after the crime. Authorities were examining the vehicle for clues in what Phoenix Police Chief Daniel Garcia called a "tragic and appalling criminal violation."
Phoenix Mayor Greg Stanton said the city was shocked and saddened.
About a dozen parishioners gathered across the street on Thursday, kneeling on the sidewalk and reciting the rosary. A bouquet of flowers and a photograph of Walker lay on the sidewalk.
The two priests lived at the church, located along a gritty stretch of downtown Phoenix near the state Capitol. Terra, 56, served as pastor and Walker, 29, as assistant pastor.
Terra called 911 to report a burglary around 9:30 p.m. Wednesday and administered last rites to the wounded Walker while waiting for police to arrive.
The Rev. Fred Adamson, vicar general of the Phoenix Diocese, said the act brought a "great deal of comfort and consolation to us as Catholics, that he was able to extend that in his own suffering."
Deacon Jim Trant, of the Diocese of Phoenix, speculated that the suspect or suspects may have just knocked on the church door to be allowed in by the priests.
Parishioner Bill Haley visited Terra in the hospital and said the priest was in critical condition but able to talk.
"He said nothing evil about the person who did this, expressed no ill will," Haley recalled.
Haley, who knew both priests well, joined others in prayer Thursday outside the church.
"He truly is a father, and he loves his parishioners deeply," Haley said of Terra. "He would care for both our spiritual as well as our physical good."
Walker was a "young priest full of energy" who loved baseball and the outdoors and would learn the names of each new parishioner and would even visit some for dinners at their homes, Haley added.
Adamson said both men believed the church "was a safe place to live."
Associated Press writer Terry Tang contributed to this report.
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