(CNN) -- A suspect arrested in last week's deadly shooting at a Catholic church admitted "involvement in the crime" while in custody, Phoenix Police Chief Daniel V. Garcia said Monday.
One priest died in the shooting and another was seriously wounded.
The suspect, Gary Michael Moran, was identified through DNA evidence recovered both at the crime scene and from a car stolen from the church, Garcia said at a news conference. Witnesses also came forth with information, he added.
Moran, 54, was arrested late Sunday at a halfway house, Garcia said. He described the suspect as a former felon with a history of violent offenses -- including aggravated assault and burglary -- who was released from prison on April 24. Since then, Moran had been "living primarily in the streets and homeless shelters," Garcia said.
In announcing the arrest, the police chief said once the suspect was in custody, Moran "made admissions to his involvement in the crime" before invoking his rights.
Garcia called the attack on the two men a "senseless act of violence" and a "vicious, tragic, horrifying" offense.
"The city of Phoenix -- waking up to this horrific crime -- felt an urgency to bring this violent, felony offender to justice. It was something we felt committed to." said Garcia.
Phoenix Mayor Greg Stanton echoed this sentiment calling the crime, "as senseless as it is tragic."
Police said they believed it was a crime of opportunity -- a burglary that went bad. At around 9 p.m. Wednesday, Terra made a 911 call reporting a burglary at the church.
According to Garcia, an intruder was discovered first by the 56-year-old Terra and the intruder allegedly attacked him with a metal rod. The suspect also reportedly managed to get a gun that belonged to the priest away from him and use it against him.
When Walker, 29, emerged from his room -- after hearing noises -- the suspect also allegedly shot him with the gun, Garcia said.
When officers arrived, they found both priests badly wounded.
Terra was able to speak briefly with the officers before being taken for treatment. Walker died on his way to the hospital, according to police.
A funeral Mass was held Monday for Walker. The service was attended by the police chief, the mayor and a local city councilman, Michael Nowakowski, as well as Walker's parishioners and members of the community.
At the news conference, the mayor noted that although Walker had not been in Phoenix "for a long period time, he had already made a lasting impact. His devotion to his church and those in his congregation meant a great deal to many of all faiths across this city."
Nowakowski spoke, saying he believed the priest would want his community to reach out and find ways to help those newly out of prison -- like Moran.
"If Father Walker were here today, he would probably say, "We need to help and pray for those individuals who are released from jail...we need to help those individuals change their heart and rehabilitate them. We as a society need to figure out a way to help those men and women who are released from jail go into a transition of hope -- not hopelessness -- and change their ways, somehow, someway.'"
Terra was moved out of intensive care over the weekend and is expected to make a full recovery, according to CNN affiliate KPHO.
CNN's Amanda Watts and Mariano Castillo contributed to this report.