"Until we can confirm that he's either there or he's not there, this investigation has to stick with what we know and what we know is that we found evidence that he was there," Neiman said.
While the LAPD spokesman told reporters he was "not ready to confirm" that a man seen in security camera video from a Southern California sporting goods store was Dorner, the Los Angeles Times quoted unnamed law enforcement sources saying it was him.
The video, published Monday by the celebrity news website TMZ.com, shows the man carrying what appears to be scuba equipment at the Sports Chalet store in Torrance, California, on February 1, two days before the killings of Monica Quan, the daughter of the police union rep, and her fiancé, Keith Lawrence.
A "no bail" arrest warrant was issued for Dorner after the Riverside County district attorney filed a murder charge Monday against him in the killing of Riverside Police Officer Michael Crain.
"That allows him to be apprehended anywhere within California, out of state or out of the country," District Attorney Paul Zellerbach told reporters Monday.
The murder charge is accompanied by two "special circumstances," including killing a police officer on duty and firing a weapon from a vehicle.
Dorner was also charged with the attempted murder of three other police officers, including another Riverside officer who was wounded when Crain was killed. That officer, whose name has not been released, is in a lot of pain and faces "many surgeries," Riverside Police Chief Sergio Diaz said.
Dorner is also accused of opening fire on two LAPD police officers, wounding one, in the suburb of Corona.
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.