The 33-year-old former policeman is thought to have exchanged fire with police after barricading himself in.

A single gunshot was later heard inside the building, which then began to burn.

One officer was killed and another injured during the shoot-out. Dorner is also accused earlier of shooting dead a young couple and a police officer.

Forensic tests will determine if the charred remains found in the razed cabin after Tuesday night’s siege are those of Dorner.

The gunman had sworn revenge on police officers he blamed for his sacking in 2008.

The search moved to the area of Big Bear Lake, a ski resort 80 miles (130km) east of Los Angeles, last Thursday after the suspect’s burnt-out truck was found there.

San Bernardino County Sheriff’s spokeswoman Cynthia Bachman said of the remains: “We have reason to believe that it is him.”

An officer briefed on the investigation told the Associated Press news agency that a driver’s licence naming Dorner was found in the burned cabin with the body.

But Los Angeles Police Chief Charlie Beck said he was not considering the situation over until tests confirmed the remains were Dorner’s.

“It is a bittersweet night,” Mr Beck told the Los Angeles Times.

Tuesday’s shoot-out began when officials from California’s wildlife agency were searching for a car reported stolen in the area.

A woman told police she had been tied up by the suspect when she and another woman had entered an empty house to clean it. She managed to get free, but he had stolen the car.

As wildlife officials searched for that stolen car, a different pickup truck sped erratically towards the officials, department spokesman Lt Patrick Foy said, with the driver firing on them.

After the truck ran off the road and crashed into a snow bank, a man matching Dorner’s description was seen running to a cabin where he barricaded himself in.

Reports say the police fired tear gas into the building and used a loudspeaker to urge the gunman to surrender.

Officials used a demolition vehicle to tear down the walls of the cabin.

Shortly afterwards, a single gunshot was heard inside the building and a fire began to spread through the cabin.

Los Angeles police officials had offered a $1m (£630,000) reward for information leading to Dorner’s arrest, receiving more than 1,000 tips.

The former Navy reservist is suspected of killing three people in a spree across southern California, including a policeman.

Police have been protecting about 50 families, many belonging to former LAPD colleagues, against whom Dorner had vowed revenge for allegedly ruining his career.

He was fired for making false statements, after making a complaint against his field training officer, saying she had kicked a suspect during an arrest.

His killing spree began on 3 February when he shot dead the daughter of a former police captain who represented him at his police disciplinary board, and her fiance.

Dorner apparently believed the woman’s father, Randal Quan, did not defend him adequately.

In an online manifesto, Dorner, who is black, suggested that racism was still rife in the LAPD.

It was an unwelcome allegation for a department that overhauled itself after the notorious police beating in 1991 of a black man, Rodney King.

At the weekend, the LAPD’s chief of police said the department would re-examine the case that led to Dorner losing his job, a key grievance in the suspect’s online essay.

He said the move was to demonstrate transparency and “not to appease a murderer”.

Reprinted from BBCnews