RIVERSIDE, California (CNN) -- Authorities said Wednesday they are reasonably sure that the body found inside the burned cabin near Big Bear Lake, California, is that of Christopher Dorner, the rogue ex-cop who had been pursuing a vendetta against his fellow officers.

"We believe that this investigation is over, at this point, and we'll just need to move on from here," San Bernardino Sheriff John McMahon told reporters.

Although the description and behavior of the man who was killed are consistent with Dorner, officials "cannot absolutely, positively confirm it was him," McMahon said.

"We're not currently involved in a manhunt," he said. "Our coroner's division is trying to confirm the identity through forensics."

Authorities say Dorner launched a guerrilla war against the Los Angeles Police Department over what he considered his unfair dismissal in 2009.

McMahon identified a sheriff's detective who was fatally shot Tuesday by the man presumed to have been Dorner as Jeremiah MacKay. MacKay, 35, was a 15-year veteran who was married with two children, a 7-year-old daughter and a 4-month-old son.

Another officer has undergone "a couple of different surgeries" after being wounded in the shootout. "He's in good spirits and should make a full recovery after a number of additional surgeries," McMahon said.

The two men were ambushed Tuesday when they responded to a report of a vehicle stolen by a suspect matching Dorner's description, McMahon said.

"It was like a war zone, and our deputies continued to go into that area and tried to neutralize and stop the threat," McMahon said. "The rounds kept coming, but our deputies didn't give up."

The suspect then fled into a nearby vacant cabin, which caught fire after police shot tear gas canisters into it, McMahon said.

Although the canisters included pyrotechnic tear gas, which generates heat, "We did not intentionally burn down that cabin to get Mr. Dorner out," McMahon said.

It wasn't clear when a formal identification could be made of the charred remains found in the cabin about 100 miles east of Los Angeles after Tuesday's shootout with police. Until then, "a lot of apprehension" remains in the ranks of the LAPD, Lt. Andy Neiman said.

'A very trying time' for the LAPD

"It's been a very trying time over the last couple of weeks for all of those involved and all those families, friends and everybody that has been touched by this incident," he said.

On Wednesday, police from around the Los Angeles area and beyond gathered to bury Michael Crain, who was among the four people fatally shot, allegedly by the 33-year-old former Navy officer.

Dorner also killed the daughter of a former LAPD captain and her fiance and shot three other officers, including Crain's partner, police say.

A squad of bagpipers led Crain's flag-draped casket through a cordon of blue uniforms into a church in Riverside, the Los Angeles suburb where the 34-year-old police officer had served 11 years on the force.

The mourners inside the church included California Gov. Jerry Brown, his Highway Patrol chief and law enforcement from a number of other agencies around the region.

"I knew that communities would reach out, and I knew a lot of people loved Mike," Regina Crain, the slain officer's widow, told them. "And I knew that I would have support no matter what. But I really did not realize the sheer scale of this, and how many people are touched by his life. It gives me really great comfort to see that, and I want to thank you all."

Investigators began scouring the mountains February 7, when investigators found Dorner's scorched pickup. Police, sheriff's deputies and federal agents swarmed into the area, working through a weekend blizzard, but the trail was cold for days.

On Sunday, the San Bernardino County Sheriff's Department said it had scaled back the search. Los Angeles Mayor Antonio Villaraigosa announced a $1 million reward for information leading to Dorner's arrest and conviction, spurring hundreds of tips.

The trail picked up again on Tuesday, when Karen and Jim Reynolds came upon a man who looked like Dorner in their house across the street from the sheriff's command center in the Big Bear area. He tied them up and took off in their purple Nissan, according to police.

The unit had been unoccupied since January 29 and they had last done some work on it on February 6, Karen Reynolds told reporters.

They returned on Tuesday to continue working on the apartment, she said. "We had come into the living room and he opened the door and came out at us," she said.

"He yelled, 'Stay calm,'" Jim Reynolds said. "When he jumped out and hollered, 'Stay calm!' Karen screamed and turned and started running and he ran after her and he caught her on the staircase and brought her back."

Dorner tried to calm them, the couple said. "He had his gun drawn the whole time," Karen Reynolds said.

He ordered them to lie down and bound their hands behind their backs with plastic ties, telling them he would not kill them, but needed transportation out of Big Bear, they said.

He then gagged them, put pillowcases on their heads and left, they said.

Throughout, he was calm, they said.

"He said I don't have a problem with you, I just want to clear my name," Jim Reynolds said.

The man then took their 2011 Nissan Rogue, they said.

It was not clear how long he had been there, a bag of carrots and milk were in the refrigerator, they said.

At around 12:20 p.m., some 15 minutes after he left, they freed themselves and called 911 to report the incident, they said.

"We're very happy to be alive," Karen Reynolds said. "I didn't wish him dead though ... I prayed for him a lot and I'm praying for his family now."

A 'guy with a big gun'

At 12:45 p.m., Fish and Wildlife wardens spotted the SUV and began pursuing it.

The wardens, driving in separate vehicles, chased Dorner, and a gunbattle ensued. One of the warden's cars was hit, and Dorner crashed his car and ran, according to authorities. He then carjacked a pickup truck.

Rick Heltebrake, a camp ranger, said he was driving when he saw the crashed purple vehicle -- and then something terrifying.

"Here comes this guy with a big gun, and I knew who it was right away," Heltebrake told CNN affiliate KTLA. "He just came out of the snow at me with his gun at my head. He said, 'I don't want to hurt you. Just get out of the car and start walking.' "

Heltebrake said the man let him take his dog and walk away with his hands up.

"Not more than 10 seconds later, I heard a loud round of gunfire," Heltebrake said. "Ten to 20 rounds, maybe. I found out later what that was all about."

Dorner fled to a nearby cabin and got into another shootout, this time with the San Bernardino County deputies, killing one and wounded another.

Some of the firefight between police and the suspect was captured live on the telephone of a reporter for CNN affiliates KCBS and KCAL. Police in Los Angeles listened live over police scanners broadcast on the Internet, LAPD Lt. Andy Neiman said.

"It was horrifying to listen to that firefight," he said. "To hear those words, 'officer down,' is the most gut-wrenching experience you can have as a police officer, because you know what that means."

Audio from a Los Angeles television station captured the sound of someone early in the standoff shouting, "Burn it down ... burn that goddamn house down. Burn it down." It's not clear who used those words.

But the order to use smoke canisters -- "burners" -- didn't come for another two hours, according to San Bernardino County sheriff's radio traffic.

"Seven burners deployed, and we have a fire," one officer reported at 4:16 p.m. (7:16 p.m. ET).

Five minutes later, a single gunshot was reported from inside the house. A senior officer ordered units around the cabin, "Stand by. Maintain your discipline." About a minute after that, officers reported ammunition exploding inside.

Sheriff's investigators confirmed overnight that they had found charred human remains among the ashes.

Dorner cheered in some quarters

Dorner had vowed to kill police officers to avenge what he called his unfair termination. He was fired after accusing his training officer of kicking a suspect during a July 2007 arrest, a complaint the LAPD concluded was unfounded.

The department accused him of lying to superiors and to internal affairs investigators and forced him out in January 2009. Dorner challenged his dismissal in court but was unsuccessful.

Dorner was first named a suspect in two shooting deaths on February 3: Monica Quan, the daughter of his police union representative, and her fiance, Keith Lawrence.

Police say he killed Crain and wounded Crain's partner in an ambush on their patrol car February 7. They say he also wounded an LAPD officer who chased him in the suburban city of Corona, California.

In a manifesto announcing his planned rampage, Dorner said nothing had changed in the LAPD since its scandals of the 1990s, the Rodney King beating and the Rampart police corruption case. Those allegations have struck a chord with some who say that, despite the four killings, Dorner was seeking justice.

Shadowed by that history, LAPD Chief Charlie Beck announced Saturday that the department would re-examine its proceedings against Dorner. The review is "not to appease a murderer," but "to reassure the public that their police department is transparent and fair in all things we do," he said.