A 69-year-old Jewish man died on Monday from injuries he suffered during a weekend altercation in Southern California over the Israel-Hamas war, and the authorities said they were investigating the incident as a homicide and a possible hate crime.

The dispute occurred Sunday afternoon amid dueling demonstrations at an intersection in Thousand Oaks, Calif., a suburb about 40 miles northwest of Los Angeles, the authorities said. Deputies from the Ventura County Sheriff’s Office responded to a call about a physical altercation at the protest site, where pro-Israeli and pro-Palestinian factions were present, according to the agency.

There, they found Paul Kessler with a head injury he had sustained when he fell backward and hit his head on the ground. Mr. Kessler, a Thousand Oaks resident, was taken to a hospital, where he died a day later. The Ventura County Medical Examiner’s Office determined that Mr. Kessler had died of blunt force head injury, the Sheriff’s Office said.