LAPD spokesman Andrew Smith urged Dorner to turn himself in.
"That would be the best resolution for this whole thing right now," he said. "No one else has to be shot. No one else has to be injured. No one else has to die. He can turn himself in anywhere, and he'll be taken into custody, and he'll be able to get his side of the story out."
Dorner, who also served in the Navy, is suspected of killing two people in Irvine, California, on Sunday and shooting Thursday at three Los Angeles-area police officers, one of whom later died.
One of the victims of the Irvine killings, Monica Quan, was the daughter of the retired police officer who represented Dorner in his efforts to get his job back, police said.
According to a criminal complaint, someone claiming to be Dorner called the retired officer after the killing, telling him he "should have done a better job of protecting his daughter."
The call was traced to Vancouver, Washington, but the complaint went on state that it was unlikely Dorner was in Washington at the time of the call.
Los Angeles Mayor Antonio Villaraigosa described Dorner as "a very sick individuaI."
"There is absolutely nothing that was done to this individual that would rationalize in any way the murder of three innocent people," Villaraigosa told CNN on Saturday. "The notion that somehow this deranged individual be given any credence boggles my mind."
For now, the focus of the manhunt remains on Big Bear and the surrounding mountains, where Dorner's burned-out pickup was found Thursday.
The truck had a broken axle, which would have prevented the truck from moving, and footprints appear to show Dorner doubled back into the community, according to a source with knowledge of the investigation.
It was unclear where Dorner may have gone from there or by what means, the source said.
Guns found in the truck also were burned, but authorities believe Dorner may have as many as 30 weapons with him, said the source, who spoke on condition of anonymity. The source was not authorized to release details to the media.
Dorner, who retired from the Navy Reserve on February 1 as a lieutenant, was trained in counterinsurgency and intelligence, the source said.
It is also believed that he received flight training during his time in the Navy. Though the exact nature of his flying skills are not known, the Transportation Security Administration issued an advisory.
"While there is no specific information at this time that Dorner is considering using general aviation, TSA requests that operators use an increased level of awareness concerning any suspicious activity during the coming days," it said.
Meanwhile, Bob Dow, supervisor at the airport at Big Bear Lake, dismissed the possibility that Dorner left that airport on a plane, saying the airport monitors all planes coming in and flying out.
Navy installations throughout California and Nevada were on heightened alert, a U.S. military official told CNN.
"Security personnel are on the lookout," said the official, who spoke on condition of anonymity. The measure was ordered late Thursday by Rear Adm. Dixon Smith, commander of the Navy's southwest region.
The official, who was not authorized to release details to the media, declined to discuss security procedures, but said the move was made after it became clear that Dorner gained access this week to the Naval Base at Point Loma and stayed in a motel there.
Two sailors reported Dorner approached them Wednesday and spoke with them for about 10 minutes at a San Diego coastal riverine unit -- a quick, small boat fighting team -- where Dorner served in 2006. As a Navy reservist, Dorner held security jobs at that unit.