There has been speculation, based in part on an arrest warrant affidavit filed last week, that Dorner could have crossed state lines into Nevada or made his way to Mexico.
LAPD reopens case that led to Dorner's dismissal
Over the weekend, LAPD said it was reopening the case that resulted in his termination.
Dorner accused his training officer of kicking a mentally ill man during an arrest in 2007. The LAPD ruled the complaint unfounded and kicked Dorner off the force for filing a false complaint.
Dorner challenged his firing in court and lost.
In a manifesto released last week, Dorner blamed racism and corruption in the LAPD for his termination and vowed to wage "unconventional and asymmetrical warfare" against LAPD officers and their families. He called it a "last resort" to clear his name and strike back at a department he says mistreated him.
LAPD Chief Charlie Beck had a different term for it Sunday.
"This is an act -- and make no mistake about it -- of domestic terrorism," he told reporters Sunday. "This is a man who has targeted those that we entrust to protect the public. His actions cannot go unanswered."
Authorities say Dorner began making good on his threats on February 3 when he allegedly killed Quan, 27, and Lawrence in an Irvine parking lot, south of Los Angeles.
According to the manifesto, Randal Quan, Monica Quan's father, bungled Dorner's LAPD termination appeal.
Randal Quan represented Dorner during the disciplinary hearing that resulted in his firing. The officer was among dozens named in the manifesto.
The retired officer told investigators he received a call from someone identifying himself as Dorner who told him he "should have done a better job of protecting his daughter," according to a federal arrest warrant affidavit.
Investigators traced the call to Vancouver, Washington, but based on the timing of other sightings, they don't believe Dorner was in Vancouver at the time, the affidavit states.
Days later, early Thursday morning, Dorner allegedly opened fire on two LAPD police officers, wounding one, in the suburban city of Corona.
Roughly 20 minutes later, Dorner allegedly fired on two officers in the nearby city of Riverside, killing Crain and wounding another.
Since then, the LAPD has provided security and surveillance details for more than 50 police officers and their families -- many of whom were named in the manifesto.
Additionally, the LAPD is no longer releasing the police chief's schedule to the public or the media.
'Ghosts' of the LAPD's past
It was Dorner's allegations of racism at the LAPD that led Beck over the weekend to reopen the investigation into his claims.
Beck said he was not doing it to "appease a murderer" but out of concern that Dorner's allegations will resurrect a painful part of the department's history.
For years, the LAPD was dogged by complaints of racism and corruption. In 1965 and 1992, the city was rocked by racial riots that were sparked, in part, by claims of police racism and brutality.
"I hear the same things you hear: The ghosts of the past of the Los Angeles Police Department," Beck said Sunday. "I hear that people think maybe there is something to what he says, and I want to put that to rest."
Despite numerous reviews of Dorner's case, he said it has "never been reviewed by me."
"If there is anything new, we will deal with it, and we will deal with it in a public way," Beck said.