Dwyer said that moment "obviously prompted some concerns in terms of what his motive may have been", but said the investigation showed Muhammad's alleged actions were "solely based on race".
He didn't want to go quietly, Dyer said.
Authorities in Fresno, Calif., have captured a suspect in the slaying of three white men who were walking on the city's streets Tuesday morning.
Muhammad spoke to his mother Tuesday night after he was arrested, Dyer said.
The men fled, and the gunman chased one of them - eventually catching up at the parking lot of Catholic Charities. The 25-year-old was shot and killed while responding to an incident at the motel Muhammad was visiting. He was a 34-years-old father and it was his first day out in the field. He added that Muhammad has a significant criminal history including drug offenses, weapons violations and making terrorist threats.
Witnesses said they saw a man carrying a large handgun, who reloaded it several times between shots. Police suspect that the man responsible for three shooting. After police left, he climbed down and went to a nearby school and hid by a trash dumpster.
It was not immediately clear why security got involved, but the woman started arguing with Carl Williams, a 25-year-old unarmed security guard, police said.
"He said he is Muslim, but prays to seven different gods", the police chief said.
Dyer said Muhammad had been identified quickly as the prime suspect in the Motel 6 shooting on April 13 and that police had been urgently seeking him across the Fresno area since then. Following that he encountered another man, who he shot and killed, according to Dyer.
Dyer says Muhammad fired at Williams, intending to kill him, because he felt Williams disrespected him.
Dyer said that the officers who responded to the scene saw a black man running. Wright says he expects the arraignment will be scheduled for Friday.
When Muhammad later saw a police auto, he surrendered.
"Dyer says Muhammad's Facebook page contains numerous anti-government posts and claims of hating white people".
He told detectives he murdered security guard Carl Williams outside a Motel 6 last week because the minimum-wage earner "disrespected him". "Victim number two is 37-year-old Mark James Gassett of Fresno", Dyer said.
Maria Praise told CNN she ran inside and locked the doors when she heard the sound of gunfire.
He had been associated with gangs but he was not a confirmed member, police say.
The suspect now faces four counts of murder and two charges of attempted murder.
He claimed insanity, and his attorney requested a psychiatric examination for his client, saying Muhammad "appeared eccentric with some freaky beliefs". According to court documents, he "suffered auditory hallucinations and had at least two prior mental health hospitalizations".
Kori Ali Muhammad surrendered himself to police Tuesday after firing multiple rounds at people in what police now consider an anti-white hate crime.
His lawyer said Muhammad had "paranoia" and thought the justice system and his defence were conspiring against him, court papers said.
Muhammad is believed to have targeted white men in Tuesday's attack.