US police fatally shot a homeless man during a "brutal" videotaped struggle in which an officer cried out that the man had grabbed his gun, the Los Angeles police chief said.

Video showed the man reaching toward the officer's waistband, police chief Charlie Beck said.

The officer's gun was found partly cocked and jammed with a round of ammunition in the chamber and another in the ejection port, indicating a struggle for the weapon.

"You can hear the young officer who was primarily engaged in the confrontation saying that 'He has my gun. He has my gun,'" Mr Beck said. "He says it several times, with conviction."

Three other officers then opened fire.

The man was black, as was the officer who was just short of completing his first probationary year on the force, police said.

Mr Beck's narrative of the shooting, including photos from video showing the condition of the gun, was a rare event just 24 hours after a shooting involving an officer. The incident came amid heightened attention to killings by police officers that have led to protests, some violent, across the country.

Sunday's violence had echoes of the August police shooting of 25-year-old Ezell Ford, whose death in a struggle with LA officers brought demonstrations in the city. Ford was unarmed, and police said he was shot after reaching for an officer's gun.

Mayor Eric Garcetti said he and the police chief needed to respond quickly to reassure residents that there is a robust investigation into the shooting, which occurred in an area that is home to the city's highest concentration of homeless people.

Video of the shooting was caught from multiple perspectives, including two witnesses recording from their phones as well as cameras worn by two of the officers who fired their weapons.

The American Civil Liberties Union called on the police department to quickly release footage shot by the officers' body cameras.

Mr Beck said the incident began when officers arrived to investigate a reported robbery and the suspect refused to obey their commands and became combative.

A security camera outside a homeless shelter about 75 feet away showed the suspect pushed over a neighbour's tent before the two engaged in an altercation.

Paramedics showed up before police. When officers arrived, they tried to speak to the suspect, who was standing near the entrance of his tent.

The suspect then turned and jumped into his tent, and officers appeared to pull it up and over him in an attempt to roust him from inside. The suspect jumped out of the tent flailing, kicking and spinning in circles before ending up on the ground.

Mr Beck said officers were in a tough situation and did not know if the suspect was arming himself. Stun guns fired at the man had "appeared to have little effect and he continued to violently resist," Mr Beck said.

One witness began filming from a closer perspective. The mobile phone video posted to Facebook has drawn millions of views.

As the man took swings, four officers wrestled him to the ground. Two other officers subdued and handcuffed a woman who had picked up a dropped baton.

The struggle became blurry and distant, but shouting could be heard, followed by five apparent gunshots.

A memorial sprung up where the shooting occurred, an area known as Skid Row. White roses were placed over a tent, blankets and clothing belonging to the dead man known as "Africa".

Tents and cardboard shelters cover the pavements of Skid Row, where an estimated 1,700 homeless people live. Many of them struggle with mental illness and addiction and are no strangers to the police.

The man, whose name was withheld, was known to have had previous encounters with officers.

The three officers who fired their weapons were veterans of the beat and had special training to deal with the homeless and mentally ill.

The shooting is being investigated by the Los Angeles Police Department's inspector general and the city's district attorney.

Activists called on governor Jerry Brown to appoint a special investigator to examine the killing.