Three New Orleans police officers have been convicted over the killing of a man, the burning of his body and the cover-up of both crimes in the chaotic aftermath of Hurricane Katrina.

A federal jury found the men guilty last night on civil rights charges after local authorities failed to prosecute. It was the first in a series of expected trials of New Orleans police officers accused of crimes during the Katrina disaster five years ago, in which a wave of looting and violence accompanied the flooding of much of the city.

A former police officer, David Warren, was convicted of manslaughter for shooting an unarmed African American man, Henry Glover, in the back. Prosecutors portrayed Warren as gung ho as he wielded his own semi-automatic rifle and erroneously told fellow officers that martial law was declared and looters could be shot.

Warren contended that he feared Glover was about to attack him as he guarded a shopping centre. But a fellow officer, who witnessed the killing, described Warren as itching to shoot someone and said that Glover was walking away when he was hit. Prosecutors had asked the jury to convict Warren of murder but it decided on manslaughter. He faces a sentence of up to life in prison.

Another officer, Greg McRae, was convicted of illegally burning Glover's body after friends of the victim bundled him into a car and took him to a local school, where a police unit was based, to seek medical help. McRae took the car and drove it behind a levee, where he set it on fire with Glover's body inside and then fired shots into the vehicle. McRae admitted torching the car but said it was due to the stress of dealing with the upheaval from Katrina.

A third officer, Travis McCabe, was found guilty of trying to cover up both crimes by writing false reports and lying to the FBI about the case. Two other police officers were acquitted of charges involving the burning of Glover's body and the cover-up.

Prosecutors welcomed the convictions in a case they portrayed as an example of disregard for the law by some New Orleans police officers during the Katrina crisis.

US attorney Jim Letten said the jury had seen through the officers' attempts to hide behind the chaos of the time. "These individuals who maintained that they were somehow acting in response to stress – I think the jury rejected that," he said.

Warren's lawyer, Julian Murray, said: "He's a good man who tried to help this city ... I don't think people understand the split-second decisions police officers have to make."

The judge in the case, Lance Africk, said: "This was a case that needed to be aired."

The justice department has charged a total of 20 New Orleans police officers over their actions during Katrina. They include six officers who face trial after the police opened fire on people attempting to flee across a bridge to escape the flood water. Two were killed and four others wounded.

Five former officers have already pleaded guilty to participating in a cover-up of that incident, including the fabrication of witnesses to falsely claim that the police had come under fire before shooting at people on the bridge.

They are being prosecuted by the federal government under civil rights legislation after local authorities proved unable or unwilling to act.

• The picture caption was amended on 28 August 2015. An earlier version said the residents in the photograph were from New Orleans. The picture was of damage left by Hurricane Katrina, but in Biloxi, Mississippi, not New Orleans.