The suspect, an African-American man named Kori Ali Muhammad, is believed to have shot a security guard last week outside a motel in the city. The guard died in hospital.
Local media quoted police chief Jerry Dyer as saying Muhammad shouted "Allahu Akbar" as he was taken into police custody yesterday, the Los Angeles Times reported.
"Too early to say whether or not this involves terrorism," Dyer was quoted as saying.
According to Dyer, Muhammad also indicated that he hated white people and the government.
Muhammad faces four counts of murder and two counts of attempted murder, authorities said.
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