Kori Ali Muhammad shot 16 rounds in 90 seconds in the shooting spree on Tuesday, said Police Chief Jerry Dyer.
He shouted "God is great" in Arabic as police arrested him but this was a hate crime not terrorism, Mr Dyer believed.
Mr Muhammad, 39, was also wanted for the murder of a security guard outside a motel in the city last week.
The suspect had indicated on social media that he hated white people and expressed anti-government views, police said.
All four victims were white men, and one of them was shot sitting in a car.
"He wanted to kill as many people as he could and that's what he set out to do," said Mr Dyer.
"This was a random act of violence. These were unprovoked attacks by an individual who was intent on carrying out homicides today."
Mr Dyer added that Tuesday's attack "has nothing to do with terrorism in spite of the statements that he [Kori Ali Muhammad] made".
"He did clarify that the reason he had made that statement was that in the event that anything did happen to him that he was in fact pledging his allegiance to God for protection."