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Updated at 3:02 a.m. ET: Authorities in Los Angeles have offered a $1 million reward for information leading to the capture of a fired LA police officer sought in connection with a series of killings and threats against his former colleagues and their families.

The reward was announced even as investigators continued to comb the snowy mountains around Big Bear Lake, where Christopher Dorner's burned out truck was found on Feb. 7, and hundreds of officers patrolled the neighborhoods where people live who were threatened by Dorner in an online screed.

Every day that Dorner is loose, said LAPD Chief Charlie Beck, is another day when the likelihood of an attack on police officers or their families increases.

"We are asking the public, 'Please help us to protect you,' " Beck said at a news conference. "Please help us to find Dorner before he is able to kill again."

Dorner is wanted in the slayings of three people and the ambush-style shooting of two others, all part of a revenge-style rampage that began last Sunday, when he allegedly shot the daughter of a police union lawyer and her fiancé in an Irvine parking garage.

The heart of the search continued to be the San Bernardino mountains where Dorner was last seen, Beck said on Sunday. Officers will also look for him near where some 50 LAPD families live who were threatened by the former policeman.

"You fish where the fish are," Beck said. "And Mr. Dorner has made his intentions very clear."

Timeline: Revenge-Plot Slayings | Read: Full Manifesto | Map: Search Locations

Police locked down a home improvement store in the San Fernando Valley, more than a hundred miles away from Big Bear, after receiving a tip that someone resembling Dorner was seen in the store. Authorities searched car-to-car and cordoned off neighborhoods in Northridge, but the move was seen as mostly precautionary.

Also on Sunday, the Riverside Police Department released the name of one of Dorner's victims. Michael Crain, 34, was ambushed by a man police believe was Dorner on April 7, as he sat with his partner at a stoplight in his patrol car.

New surveillance video captures fugitive ex-cop Christopher Dorner the morning after his first two murders, NBC's Miguel Almaguer reports.

Crain, who was born in Anaheim, was an 11-year veteran of the Riverside police force. He leaves behind a wife and two small children.

A second reward, worth $100,000, could also be on the way, a spokesman for Los Angeles County Supervisor Mike Antonovich said Sunday.

Tony Bell said that Antonovich and fellow supervisor Mark Ridley-Thomas planned to ask colleagues on the Board of Supervisors to approve that reward for information leading to Dorner's capture at their meeting on Tuesday.

News of the rewards came as the LAPD announced it would re-open its investigation into Dorner’s firing from the department in 2008.

In a 11,400 word manifesto published on line, the ex-officer blamed his killing spree on his termination, saying that he would only stop when his name was cleared.

Re-opening the investigation seems to have two purposes: to communicate to members of the public who have responded to Dorner’s complaints that the LAPD treated him unfairly, and to send a message to the ex-officer himself.

Los Angeles officials announce a one million dollar reward for information leading to the arrest and conviction of former LAPD officer Christopher Dorner.

The department "is not opening it because of the accusations or because of the musings of someone who is a multiple murderer now," Cmdr. Andrew Smith said Saturday. Chief Charlie Beck is "wants to ensure that the public knows that the Los Angeles Police Department is fair and transparent, " Smith said.

Witnesses will be re-interviewed and the investigation into Dorner's firing will get a "fresh set of eyes," Smith said. He also issued a plea for Dorner to come forward.

"He can turn himself in and he can be able to get his side of the story out," Smith said.

Deputies have been combing the ski resort area of Big Bear, where authorities found former LAPD Officer Christopher Dorner’s burned-out truck, since Thursday afternoon.

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Investigators found weapons inside the truck, suggesting Dorner may have abandoned the truck in an unplanned hurry.

Former LAPD Chief William Bratton told the "Today Show" on Saturday that evidence suggests Dorner's truck may have become stuck in the mud. Previously, it was speculated that the truck may have been intentionally set ablaze as a distraction.

Investigators on Saturday were also trying to determine whether the truck's axle was broken when they found it, or if it was fractured while being towed from the forestry road.

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Los Angeles Mayor Antonio Villaraigosa, interviewed outside a prayer breakfast downtown, urged Dorner to turn himself in.

"We will find you," Villaraigosa said. "You’ve disgraced the public safety -- the police profession -- turn yourself in."

As the search in Big Bear was winding down for the night on Saturday, LAPD announced the department is reopening the case into Dorner's 2008 firing from the force.

In an 11,400-word document published online, Dorner laid out plans to kill law enforcement officers and their families, vowing to stop the attacks when LAPD "states the truth about my innocence."