Tracy Province and John McCluskey have not strayed far from the medium-security prison where they cut through a fence Friday and took off, police say.
Authorities have named McClusky's fiancee, Casslyn Mae Welch, as an accomplice who allegedly helped the men escape and is helping them stay on the run.
"It is thought that they are still in the region, in Arizona," state Department of Corrections Director Charles Ryan said.
A third escaped convict, Daniel Renwick, is being questioned by the FBI after being captured Sunday in Colorado following a shootout with police.
Police have said they were no longer looking for a 2002 silver Volkswagen Jetta that they believed the prisoners may have bought off Craigslist, but gave no explanation.
Province, McClusky and Welch were last spotted in Phoenix Saturday, withdrawing money from ATMs.
"Hopefully, they'll surrender, and their families will talk to them and give them good advice," Chief Deputy U.S. Marshall Fidencio Rivera said. "We don't want anybody to get hurt."
While authorities from several agencies hunt for McClusky and Province, officials with the Department of Corrections are scrambling to tighten security at the prison, where the escape is being blamed on a combination of lax guards and a failed alarm system.
Officials blamed the breakdown on a private company from Utah that operates the security system at Arizona State Prison-Kingman in Golden Valley. An alarm failed, they said, on the door that the inmates passed through. Although a second alarm sounded when the inmates cut through the fence, the guards apparently failed to notice.
"My concern is the staff at this prison may have been lax in their job," Ryan said, "and that probably created the opportunity so that they could escape."
Shortly after their escape, the convicts kidnapped two big-rig drivers at gunpoint and demanded to be taken to Flagstaff, Ariz. The drivers were later released unharmed.
Province was serving a life sentence for murder and robbery. McClusky was serving 15 years for second-degree murder, aggravated assault and discharge of a firearm, the Associated Press reported.
Renwick had been serving a 22-year sentence for second-degree murder.
"We believe they are armed and dangerous," Rivera said.
While questions have been raised about why convicted murderers were assigned to a medium-security prison, officials said the placement was because of time served and good behavior.
The Associated Press contributed to this story.