LOS ANGELES — A gunman thought to be a fugitive ex-police officer shot and killed one police officer and wounded another in a gun fight with sheriff’s deputies who tracked him down to a mountain cabin northeast of Los Angeles on Tuesday, police said.

Authorities said they presumed the shooter to be former Los Angeles police officer Christopher Dorner, 33, who is suspected of a revenge-fueled killing spree targeting police and their families. Television news footage showed smoke and flames engulfing the cabin in a heavily wooded area of the snow-covered mountains of the San Bernardino National Forest.

A body found in the burned-out cabin was believed to be Dorner, CBS News and the Los Angeles Times reported.

San Bernardino County sheriff’s spokeswoman Cindy Bachman said a “smoke bomb” had been set off at the cabin before the fire started, but she was uncertain if it had been detonated by the gunman or law enforcement authorities.

“There is a subject barricaded in the cabin and at this time that cabin is on fire,” Bachman said in a televised news briefing. “If there is someone inside the house, he is armed and already killed one of our sheriff’s deputies, so we’re not going to allow anyone to go near that house.”

Police said the man they believe to be Dorner surfaced for the first time in several days after breaking into a home near the ski resort community of Big Bear Lake, tying up a couple there and stealing their pickup truck.

A state game warden apparently on the lookout for Dorner exchanged gunshots with the driver of the stolen truck. The vehicle later was abandoned and the driver fled into the forest.

Officials of the San Bernardino County Sheriff’s Department said the gunman barricaded himself inside another cabin and engaged in a shootout with police as they closed in on him.

One San Bernardino County sheriff’s deputy was shot and killed and another was wounded, Sheriff John McMahon told reporters.

Los Angeles Police Chief Charlie Beck has called the search for Dorner the most extensive manhunt in the region’s history.

Dorner’s last confirmed encounter with authorities came early last Thursday, when police said he ambushed two policemen at a traffic light in Riverside, about 60 miles east of Los Angeles. One of those officers was killed and the other wounded.

Dorner, a former Navy officer, is also suspected of having exchanged gunfire with police and wounding one officer in nearby Corona.

Last Wednesday, he was named as a suspect in the slayings of a campus security officer and his fiancee, the daughter of a retired Los Angeles Police Department captain. In a manifesto posted on his Facebook page last week, Dorner blamed the captain for his 2008 dismissal from the LAPD.

The couple, Keith Lawrence, 27, and Monica Quan, 28, an assistant college basketball coach, were found shot dead on Feb. 3 in their car on the top level of a parking structure in the city of Irvine, south of Los Angeles.

Quan’s father, Randy Quan, had represented Dorner in disciplinary proceedings that led to his dismissal after a police inquiry found Dorner had made false statements accusing a superior officer of using excessive force, police said.

In the rambling online declaration, Dorner claimed he had been wrongly terminated and vowed to seek revenge by unleashing “unconventional and asymmetrical warfare” on police officers and their families.

Riverside County Prosecutors formally charged Dorner on Monday with one count of first-degree murder and three counts of attempted murder in connection with last Thursday’s shootings of police officers.

On Sunday, authorities posted a $1 million reward for information leading to Dorner’s capture. They said it was the largest such amount ever offered in a Southern California criminal investigation.