The man who was shot and killed by an off-duty Los Angeles police officer at a Costco in Southern California on Friday was known as a "gentle giant" who was mentally disabled and couldn't have started an argument that led to the deadly confrontation, his cousin said Sunday.

The Corona Police Department said 32-year-old Kenneth French from Riverside was shot dead after he allegedly "assaulted the officer while the officer was holding his young child," which led to the cop firing his weapon, striking French and two other family members who were critically wounded.

But his cousin, Rick Shureih, disputes the account released by authorities, telling the Press-Enterprise that French was "non-violent, non-aggressive, nonverbal" and a "gentle giant."

“He’s not the kind to trade words, so I don’t believe that a verbal confrontation happened," he told the paper.

OFF-DUTY LAPD OFFICER FIRED FATAL SHOT IN CALIFORNIA COSTCO SHOOTING

Shureih, who was not at the store at the time of the shooting, identified the other victims to the Press-Enterprise as French's parents, Russell and Paola French, saying they remained in an intensive care unit Sunday. Authorities have not released their names.

He posted a photo to Facebook on Sunday saying he was "not keeping quiet about this" because "people need to know!"

"Do they look intimidating to you? Did he really have to shoot them all? I’m posting this picture because the stories on social media have made them out to be the suspects, and the off duty cop the victim," Shureih said. "This is a family that was unarmed and was just grocery shopping. Truth will come out! I’m sure this was a misunderstanding that got escalated for no reason!

In a separate interview with the Los Angeles Times, Shureih said his cousin's mental condition had declined in recent years and that he no longer spoke.

“It could have been that he bumped into somebody but couldn’t communicate the fact that he was sorry,” Shureih said.

The cousin said the family is working on hiring a lawyer and is seeking the name of the off-duty officer, as well as surveillance video and witness accounts to try to understand what happened, FOX11 reported.

COSTCO STORE GUNFIRE LEAVES 1 DEAD, 2 INJURED IN SOUTHERN CALIFORNIA

Police have not said if French had any weapons or if the officer identified himself as a member of the police before firing.

"As is standard procedure in such investigations, the Corona Police Department is working closely with the Riverside County District Attorney’s Office, who will be evaluating the facts and circumstances of this incident," Corona police said Saturday.

The shooting at the Costco about 40 miles east of Los Angeles Friday night prompted a stampede of frightened shoppers, some who fled the store as others sought cover inside. Witnesses reported seeing an argument between two people near a freezer section when shots rang out at least six times.

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The LAPD will continue its internal probe as Corona police and the Riverside County district attorney's office conduct a separate investigation into the shooting. The LAPD said Sunday it had no further information. A Corona Police Department spokesperson told Fox News on Monday that a "very serious active investigation" is underway, and there was no new information since a press release was issued Saturday night.

Los Angeles Police Commission President Steve Soboroff said Sunday it is Chief Michel Moore's decision whether to put the officer on leave, but it remained unclear if that happened.

The off-duty officer -- assigned to the Los Angeles Police Department's Southwest Station -- suffered minor injuries in the incident and was released at a nearby hospital, Officer Greg Kraft of the LAPD's Media Relations Section told FOX11. His child was not injured during the incident.

The department's policies allow off-duty officers to carry concealed weapons as long as they are authorized for on-duty use, according to the LAPD manual.

Fox News' Brie Stimson and the Associated Press contributed to this report.