Thousand Oaks, California - California police briefly detained a pro-Palestinian protester over the death of a Jewish man following a confrontation between two rival rallies over the Israel-Gaza war, but no arrest has been made, officials said Tuesday.

Ventura County sheriff James Fryhoff said Paul Kessler's death from a head injury after falling to the ground "is being investigated as a homicide," and investigators have not yet ruled out the possibility of a hate crime.

A search warrant was obtained for a 50-year-old local man who attended a rally "advocating for Palestine," and admitted to being involved in an "altercation" with Kessler, Fryhoff told a press conference.

However, "the suspect has not been arrested. No arrests have been made related to this incident," he said.

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The incident took place during dueling pro-Israel and pro-Palestinian rallies involving around 100 people on Sunday in Thousand Oaks, just northwest of Los Angeles.

Police arriving at the scene found that Kessler (69) had fallen backward and fatally struck his head on the ground. He also had non-lethal injuries on his face, although it was not clear if he had been struck, said medical examiner Christopher Young.

"What exactly transpired prior to Mr Kessler falling backward isn't crystal clear right now," said Fryhoff.

The suspect "willingly remained at the scene," and told police he was among those who phoned 911 for medical assistance.

Several witnesses from both rallies "provided conflicting statements about what the altercation, and who the aggressor, was," said Fryhoff.

Kessler died in the hospital early Monday. The suspect was detained at a traffic stop later that day, while his home was searched, and interviewed again.

The incident comes a month after Hamas launched a vicious assault on Israel from the Gaza strip, killing 1,400 people, mostly civilians, and taking over 240 hostages, according to Israeli authorities.

Israel's retaliation, which has involved an extensive bombing campaign and an intensifying ground invasion of the besieged Gaza Strip, has now claimed more than 10,000 lives, according to the Hamas-run health ministry.

Calls by Arab nations for a ceasefire and an end to the blockade of Gaza have been rejected by Israel, which says it is fixed on neutralizing Hamas and rescuing the hostages.

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Los Angeles Mayor Karen Bass on Tuesday called Kessler's death "a blow to our region at a time when tensions continue to rise worldwide."

"As details emerge and are confirmed, we stand resolute in condemnation of violence and antisemitism," she said.

Fryhoff said patrols would be stepped up around local mosques and synagogues.