A major manhunt is under way in the United States for an ex-Los Angeles Police Department (LAPD) officer who authorities say embarked on a killing spree to punish those he blamed for his firing.

Christopher Dorner, a former police officer, has promised revenge against the entire LAPD and their families. 

San Bernardino County Sheriff John McMahon said officers were going door to door looking for him.

"Our state and federal partners are with us as well, and we have deputy sheriffs from other stations in the county up here providing additional patrols to the citizens of this community," McMahon said on Monday.

'Three states on alert'

The search for Dorner had three states and Mexico on alert before shifting Thursday afternoon to the snowy mountains around Big Bear Lake, about 128 kilometres east of Los Angeles, where police found his burned-out pickup truck.

Authorities say they found tracks around the truck but they did not lead to Dorner.

Schools were put on lockdown while investigators examined the vehicle and spread out across the area.

Dorner was believed to be heavily armed and wearing military-style fatigues and body armour.

The search for Dorner, who was fired from the LAPD in 2008 for making false statements, began after he was linked to a weekend killing in which one of the victims was the daughter of a former police captain who had represented him during the disciplinary hearing.

Monica Quan and her fiance, Keith Lawrence, were found shot in their car at a parking structure at their condominium on Sunday in Irvine.

Police said Dorner implicated himself in the couple's killings in the manifesto posted on Facebook.

The LAPD dispatched some of its officers to protect more than 40 other potential targets listed in the manifesto.

Source: Al Jazeera and agencies