LOS ANGELES — A man police believe to be the fugitive ex-Los Angeles officer wanted in three killings was barricaded inside a burning cabin Tuesday after a shootout in a California mountain town Tuesday that left one deputy dead and another wounded.

The developments raised the possibility that the nearly week-old hunt for America’s most wanted man might be coming to an end.

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.

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 both lower tensions among the more than 40 targets police say he listed in an online rant. It would also raise them for law enforcement officers who are engaged in a standoff with a former Navy reservist who has warned that he knows their tactics as well as they do.

Until Tuesday, authorities didn’t know whether he 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 a cabin.

U.S. Forest Service spokesman John Miller said the first exchange of gunfire involved state Fish and Wildlife wardens at 12:42 p.m., and then there was a second exchange with San Bernardino County sheriff’s deputies, two of whom were shot.

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.