Search for ex-cop at center of LAPD revenge plot widens NEW: LAPD chief promises to personally review the firing of Christopher Dorner NEW: Dorner, 33, is accused of killing a police officer He also is accused of killing the daughter of a former LAPD officer Authorities are offering a $1 million reward for information leading to an arrest Los Angeles (CNN) -- As the manhunt for the renegade ex-cop accused of killing three people in a revenge plot targeting the Los Angeles Police Department entered its second week on Monday, the big question facing authorities -- where is Christopher Jordan Dorner? The search, considered one of the largest in the history of Southern California, has taken authorities from Orange County to the border of Mexico, from Los Angeles to the Big Bear Lake resort area of the San Bernardino Mountains. Even so, a week after Dorner allegedly began targeting police officers and their families, putting the region on edge, there was no sign of the man who has left the region on edge after he allegedly began targeting police and their family members. A $1 million reward was offered Sunday for information leading to the capture and conviction of Dorner, an announcement that followed news that the LAPD 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 booted Dorner off the force for filing a false complaint. He 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 during a televised news conference. This is a man who has targeted those that we entrust to protect the public. His actions cannot go unanswered. Timeline in manhunt Authorities say Dorner began making good on his threats on February 4 when he allegedly killed Monica Quan and her fiancé, Keith Lawrence, in an Irving parking lot, south of Los Angeles. Quan is the daughter of a now-retired Los Angeles police officer, who 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 that 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. Roughly 20 minutes later, Dorner allegedly fired on two officers in the nearby city of Riverside, killing one and wounding another. On Sunday, authorities identified the slain officer as Michael Crain, an 11-year veteran of the Riverside Police Department. 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 making good on his threats to kill police and their family members. Search continues The search was scaled back in the mountain resort community on Sunday. None of the tips the department had received so far has panned out, San Bernardio County sheriff's spokeswoman Lehua Pahia said. Even so, Beck said the search would continue to focus on Dorner's last known locations in the Big Bear area. "But our search continues in and around the area where we have known targets," Beck said. But there has been speculation, based in part on an arrest warrant affidavit filed last week, that Dorner could have crossed states 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," Bill L. Lewis, the assistant director of the FBI's Los Angeles division. Police were also chasing down a number of 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 LAPD It's Dorner's allegations of racism at the LAPD led Beck over the weekend to reopen the investigation into his claims. Beck said he was not doing it "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, among 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 it 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 it and we will deal with it in a public way," Beck said. LAPD haunted by past CNN's Matt Smith contributed to this report. Paul Vercammen and Stan Wilson reported from Big Bear Lake, and Chelsea J. Carter wrote from Atlanta.