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 supporters of Israel and Palestine 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.

Witnesses told investigators that Mr. Kessler had a physical altercation with at least one counterprotester, the authorities said.

Jim Fryhoff, the Ventura County sheriff, has scheduled a news conference for Tuesday morning in Thousand Oaks.

Word of Mr. Kessler’s fall ricocheted quickly across communities that were already on edge. Several mourners on Monday night brought flowers and lit candles on a ledge outside a Shell gas station near where the altercation occurred.

Rabbi Michael Barclay, of the nearby Temple Ner Simcha, said on Monday evening that he had been urging congregants not to share rumors and that he had previously discouraged community members from counter-protesting at pro-Palestinian demonstrations to avoid confrontations.

Hussam Ayloush, the executive director of the Council on American-Islamic Relations office in Los Angeles, denounced all violence and urged people to avoid “sensationalizing such a tragedy for political gains or spreading rumors that could unnecessarily escalate tensions that are already at an all-time high.”

“We urge everyone to wait for the Ventura County Sheriff’s Office to complete its investigation before drawing any conclusions,” Mr. Ayloush said in a statement. “Our thoughts are with the family and the Jewish community during this difficult time.”

The Jewish Federation of Greater Los Angeles pointed to recent instances of antisemitic crimes in the region, which have rattled Jewish residents in Southern California.

“The fact of the matter is there is now a Jewish man who is dead,” said Rabbi Noah Farkas, the president and chief executive of the federation. “And here we are again as a Jewish community, frightened, terrified to express ourselves, to be ourselves.”

Shawn Hubler contributed reporting.