WASHINGTON — The police officer who fatally shot Michael Brown in Ferguson, Mo., two months ago has told investigators that he was pinned in his vehicle and in fear for his life as he struggled over his gun with Mr. Brown, according to government officials briefed on the federal civil rights investigation into the matter.

The officer, Darren Wilson, has told the authorities that during the scuffle, Mr. Brown reached for the gun. It was fired twice in the car, according to forensics tests performed by the Federal Bureau of Investigation. The first bullet struck Mr. Brown in the arm; the second bullet missed.

The forensics tests showed Mr. Brown’s blood on the gun, as well as on the interior door panel and on Officer Wilson’s uniform. Officer Wilson told the authorities that Mr. Brown had punched and scratched him repeatedly, leaving swelling on his face and cuts on his neck.

This is the first public account of Officer Wilson’s testimony to investigators, but it does not explain why, after he emerged from his vehicle, he fired at Mr. Brown multiple times. It contradicts some witness accounts, and it will not calm those who have been demanding to know why an unarmed man was shot a total of six times. Mr. Brown’s death continues to fuel anger and sometimes-violent protests.

In September, Officer Wilson appeared for four hours before a St. Louis County grand jury, which was convened to determine whether there is probable cause that he committed a crime. Legal experts have said that his decision to testify was surprising, given that it was not required by law. But the struggle in the car may prove to be a more influential piece of information for the grand jury, one that speaks to Officer Wilson’s state of mind, his feeling of vulnerability and his sense of heightened alert when he killed Mr. Brown.

Police officers typically have wide latitude to use lethal force if they reasonably believe that they are in imminent danger.

The officials said that while the federal investigation was continuing, the evidence so far did not support civil rights charges against Officer Wilson. To press charges, the Justice Department would need to clear a high bar, proving that Officer Wilson willfully violated Mr. Brown’s civil rights when he shot him.

The account of Officer Wilson’s version of events did not come from the Ferguson Police Department or from officials whose activities are being investigated as part of the civil rights inquiry.

In the many accounts of Mr. Brown’s death, the most potent imagery has come from his final moments, when he and Officer Wilson faced each other on Canfield Drive. Some witnesses have said that he appeared to be surrendering with his hands in the air as he was hit with the fatal gunshots. Others have said that Mr. Brown was moving toward Officer Wilson when he was killed.

Few witnesses had perfect vantage points for the fight in the car, which occurred just after noon on Aug. 9. Mr. Brown was walking down the middle of the street with a friend, Dorian Johnson, when Officer Wilson stopped his S.U.V., a Chevy Tahoe, to order them to the sidewalk.

Within seconds, the encounter turned into a physical struggle, as the officer and Mr. Brown became entangled through the open driver’s-side window.

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One witness, Piaget Crenshaw, said later that while she could not see clearly, it appeared Mr. Brown was “trying to flee.” Another witness, Tiffany Mitchell, said that she had watched with alarm from a close distance and that as the two briefly struggled, “Michael was pulling off and the cop was trying to pull him in.”

Michael T. Brady, who lives nearby, said that the altercation was “something strange,” but that he could not tell exactly what was happening. “I can’t say whether he was punching the officer or whatever,” Mr. Brady said. “But something was going on in that window, and it didn’t look right.”

However, Mr. Johnson’s description of the scuffle is detailed and specific, and directly contradicts what Officer Wilson has told the authorities.

Mr. Johnson has said that Officer Wilson was the aggressor, backing up his vehicle and opening the door, which hit Mr. Johnson and Mr. Brown and then bounced back.

“He just reached his arm out the window and grabbed my friend around his neck, and he was trying to choke my friend,” Mr. Johnson told reporters after the shooting. “He was trying to get away, and the officer then reached out and grabbed his arm to pull him inside the car.”

Officer Wilson then drew his weapon, Mr. Johnson said, and threatened to shoot.

“In the same moment, the first shot went off,” he said. “We looked at him. He was shot. There was blood coming from him. And we took off running.”

Never, Mr. Johnson said, did Mr. Brown reach for the officer’s weapon.

The officials briefed on the case said the forensic evidence gathered in the car lent credence to Officer Wilson’s version of events. According to his account, he was trying to leave his vehicle when Mr. Brown pushed him back in. Once inside the S.U.V., the two began to fight, Officer Wilson told investigators, and he removed his gun from the holster on his right hip.

Chief Jon Belmar of the St. Louis County Police Department has said in interviews that Officer Wilson was “pushed back into the car” by Mr. Brown and “physically assaulted.” The department is conducting the local investigation into Mr. Brown’s death.

Spokesmen for the F.B.I. and the Justice Department declined to comment.