Since then, the LAPD has provided more than 50 police officers and their families -- many of whom were named in the manifesto -- with security and surveillance details.
Additionally, the LAPD is no longer releasing the police chief's schedule to the public or the media.
Beck refused to discuss whether Dorner had been observed in the neighborhoods of any of those named in the manifesto, but added: "You fish where the fish are, and Mr. Dorner has made his intentions very clear."
In recent days, the search for the 270-pound, 6-foot Dorner has been focused on the Big Bear Lake area, where authorities say his burning truck was discovered last week after he allegedly began carrying out his threats to kill police and their family members.
The search in Big Bear continued Monday night into Tuesday morning, the San Bernardino County sheriff's department said. About 30 officers are searching for Dorner, police said.
There have been no sightings of Dorner in the Big Bear area, the news release said.
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.
Federal authorities, meanwhile, were asking anyone across the country with information about Dorner or his whereabouts to contact their local FBI or U.S. Marshals Service.
"Should any citizen have information, I encourage you to make that phone call," said Bill L. Lewis, the assistant director of the FBI's Los Angeles division.
Police were also chasing down unconfirmed sightings of Dorner, including one Sunday in the San Fernando Valley after two people reported seeing someone who resembled the former police officer inside a Lowes home improvement store.
The store in Northridge was evacuated, but there was no sign of Dorner.
The LAPD, meanwhile, also beefed up security at the Grammy Awards on Sunday "out of an abundance of caution," police Cmdr. Andy Smith said.
'Ghosts' of the LAPD's past
It's 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.