The suspect, a 39-year-old African-American named Kori Ali Muhammad, shouted "Allahu Akbar" -- "God is great" in Arabic -- as he was being taken into custody.
But Fresno police chief Jerry Dyer said indications were it was not a "terrorist-related crime" and a probe was under way to determine if the murders qualified as a hate crime.
He said Muhammad, who used the alias "Black Jesus" and was wanted in the killing last week of an unarmed security guard outside a motel in the city, had indicated in postings on his Facebook page that he hated white people and the government.
He said all the victims were white males and there was every reason to believe Muhammad had acted alone.
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Muhammad's father, Vincent Taylor, told The Los Angeles Times that his son was convinced he was part of an ongoing war between whites and blacks, and that "a battle was about to take place."
A Facebook page for a Kori Ali Muhammad in Fresno featured images extolling black nationalism and making repeated references to "white devils," the newspaper said.
Muhammad faces four counts of murder and two counts of attempted murder, authorities said.
Dyer said yesterday's shooting spree began in downtown Fresno when one man sitting in a truck was shot through the passenger window.
The other victims were shot nearby during a rampage that lasted about a minute and during which up to 16 rounds were fired.
Dyer said Muhammad surrendered to police at the scene, telling officers "you guys are looking for me."
Dyer said Muhammad had a criminal history including for weapons violations, drugs and making terrorist threats.
Lieutenant Mark Hudson, a police spokesman, told AFP the weapon used in the killings had not been recovered.
Hudson said the FBI had been contacted about the killings. But a spokeswoman for the FBI declined comment, referring media inquiries to local police.
The rampage is likely to reignite a long-running debate in the US on gun control, an issue that has dogged successive administrations.
More than 30,000 people are killed by gun violence in the United States every year, half of them between the ages of 18 and 35, according to statistics.
It said the victims include at least 184 children up to 11 years old and 914 teenagers between the ages of 12 and 17.
President Donald Trump has yet to spell out his policy on gun control. With Republicans in control of the White House and Congress, some critics fear his administration will ease restrictions.
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