BIG BEAR LAKE, Calif. — The man believed to be fugitive ex-cop Christopher Dorner never came out of a California mountain cabin, and a single shot was heard inside before the cabin was engulfed in flames, a law enforcement official told The Associated Press.

The law enforcement official requested anonymity because of the ongoing investigation.

A fourth person — a deputy — died earlier in the latest confrontation with America’s most-wanted man, which seemed to be coming to an end.

Officials were waiting for the fire to burn out before approaching the ruins to search for a body.

“We have reason to believe that it is him,” San Bernardino County sheriff’s spokeswoman Cynthia Bachman said.

The cabin was on fire and smoke was coming from the structure in the late afternoon after police surrounded it in the snow-covered woods of Big Bear, a resort town about 80 miles east of Los Angeles.

Bachman didn’t say how the fire started but noted there was gunfire between the person in the cabin and law enforcement officers around the home before the blaze began.

TV helicopters showed the fire burning freely with no apparent effort to extinguish it.

Authorities have focused their hunt for Christopher Dorner there since they said he launched a campaign to exact revenge against the Los Angeles Police Department for his firing.

Authorities say Dorner threatened to bring “warfare” to LAPD officers and their families, spreading fear and setting off a search for him across three states and Mexico.

“Enough is enough. It’s time for you to turn yourself in. It’s time to stop the bloodshed,” LAPD Cmdr. Andrew Smith said earlier in the day at a news conference held outside police headquarters in Los Angeles, a starkly different atmosphere than last week when officials briefed the news media under tight security with Dorner on the loose.

If the man inside the cabin does prove to be Dorner, it will lower tensions among the more than 40 targets police say he listed in an online rant.

Until Tuesday, authorities didn’t know whether Dorner was still near Big Bear, where they found his burned-out pickup last week.

Around 12:20 p.m. Tuesday, deputies got a report of a stolen vehicle, authorities said. The location was directly across the street from where law enforcement set up their command post on Thursday and not far from where Dorner’s burned-out pickup was abandoned.

The people whose vehicle was stolen described the suspect as looking similar to Dorner. When authorities found the vehicle, the suspect ran into the forest and barricaded himself inside the cabin.

The first exchange of gunfire occurred about 12:45 p.m.

California Department of Fish and Wildlife said in a statement that one of its officers traveling down Highway 38 recognized a man who fit Dorner’s description traveling in the opposite direction.

The wildlife officer pursued the vehicle and there was a shooting in which the wildlife vehicle was hit numerous times and the suspect escaped on foot.

There was then a second exchange with San Bernardino County deputies, two of whom were shot. One died and the other was expected to live after undergoing surgery.

“We’re heartbroken,” Big Bear Lake Mayor Jay Obernolte said of the deputy’s death and the wounding of his colleague. “Words can’t express how grateful we are for the sacrifice those men have made in defense of the community and our thoughts and prayers are with them and their families.”

Police say Dorner began his run on Feb. 6 after they connected the slayings of a former police captain’s daughter and her fiance with an angry Facebook rant they said he posted. Threats against the LAPD led officials to assign officers to protect officers and their families.

Within hours of the release of photos of the 6-foot, 270-pounder described as armed and “extremely dangerous,” police say, Dorner unsuccessfully tried to steal a boat in San Diego to flee to Mexico and then ambushed police in Riverside County, shooting three and killing one.

Jumpy officers guarding one of the targets named in the rant in Torrance on Thursday shot and injured two women delivering newspapers because they mistook their pickup truck for Dorner’s.

Police found charred weapons and camping gear inside the truck in Big Bear.

Helicopters using heat-seeking technology searched the forest from above while scores of officers, some using bloodhounds, scoured the ground and checked hundreds of vacation cabins — many vacant this time of year — in the area.

A snowstorm hindered the search and may have helped cover his tracks, though authorities were hopeful he would leave fresh footprints if hiding in the wilderness.

Dorner’s anger with the department dated back at least five years, when he was fired for filing a false report accusing his training officer of kicking a mentally ill suspect. Dorner, who is black, claimed in the rant that he was the subject of racism by the department and fired for doing the right thing.

He said he would get even with those who wronged him as part of his plan to reclaim his good name.

“You’re going to see what a whistleblower can do when you take everything from him especially his NAME!!!” the rant said. “You have awoken a sleeping giant.”

Chief Charlie Beck, who initially dismissed the allegations in the rant, said he would reopen the investigation into his firing — not to appease the ex-officer, but to restore confidence in the black community, which long had a fractured relationship with police that has improved in recent years.

One of the targets listed in the manifesto was former LAPD Capt. Randal Quan, who represented Dorner before the disciplinary board. Dorner claimed he put the interests of the department above his.

The first victims were Quan’s daughter, Monica Quan, 28, a college basketball coach, and her fiance, Keith Lawrence, 27. They were shot multiple times in their car in a parking garage near their condo.

Dorner served in the Navy, earning a rifle marksman ribbon and pistol expert medal. He was assigned to a naval undersea warfare unit and various aviation training units, according to military records. He took leave from the LAPD for a six-month deployment to Bahrain in 2006 and 2007.