"We do not believe ... that this is a terrorist-related crime", Dyer told reporters.
The suspect who police say took three lives in downtown Fresno, Calif., had meant to go on a lethal rampage once he found out that he was being sought for an earlier homicide, police say.
Dyer said Muhammad has been arrested in the past on weapons, drugs and false imprisonment charges and making terrorist threats.
Once he saw the officers on the scene, Muhammad got on the ground, Dyer said Tuesday.
Dyer says Muhammad told investigators that he wanted to be known as someone who killed many white people and not just a security guard.
Kori Ali Muhammad, a gunman who nicknamed himself "Black Jesus" shot and killed three strangers in a bid to kill as many white people as possible, police said.
Muhammad had a long criminal history and filled his social media feeds with posts about black separatism, reparations and "white devils".
"He said he is Muslim, but prays to seven different gods", the police chief said.
He then set his sights on three white men standing at a bus stop. Muhammad had gone there to meet a woman, and he argued with security who asked him to leave.
Muhammad, who was born Cory McDonald, is alleged to have fired 16 rounds in a shooting spree lasting less than two minutes.
He had at least two prior mental health hospitalizations, and his attorney said in court papers that Muhammad thought the justice system and his own lawyer were conspiring against him.
On Tuesday, police said, he acted on that hatred.
He allegedly pointed the gun at three Hispanic females - a woman, her adult daughter and her 4-year-old granddaughter - who heard the gunshots and got into their vehicle, which then had trouble starting.
Witness Maria Praise told CNN she ran inside and locked the doors when she heard the sound of gunfire.
Police chief Jerry Dyer briefs reporters in Fresno, Calif., after shootings on Tuesday.
In the meantime, new information about the victims of the deadly rampage is being released.
Muhammad is also accused of firing at a 59-year-old white man coming out of a house, but he missed, the police chief said. When he was taking our police officers, our detectives, to various locations to last night and yesterday.
Police believe Muhammad killed a Motel 6 security guard, Carl Williams. He continued saying that this shooting was "unprovoked". Wright says he expects the arraignment will be scheduled for Friday.
Muhammad, 39, will face four counts of murder and two counts of attempted murder, officials said.
Friend Eddie Valencia said Randalls was excited to start work as a customer-service representative and was doing a ride-along Tuesday. The driver wasn't hit and sped toward the police department, but his partner couldn't be saved.
On Monday he wrote to Facebook "MY KILL RATE INCRESASES TREMENDOUSLY ON THE OTHER SIDE ASÈ ALLAH U AKBAR".
Muhammad told his family there was a war going on between blacks and whites in America.
Utility company PG&E said in a statement that one of the victims had been an employee.
Monique Skinner tells The Fresno Bee (http://bit.ly/2osozFS ) that she was outside her apartment when she flipped the victim over and he gasped and died.
He then continued to the area of Catholic Charities where he shot and killed a person in the parking lot, police said.
During the shooting rampage, Muhammad fired several times at two Hispanic women in a auto, but he stopped shooting once he realized they were Hispanic and let them go, Dyer said.
On Tuesday morning, Muhammad had gone to buy items to practice voodoo rituals when he went to Starbucks instead, Dyer said.
The shooting began around 10:45 local time near the headquarters for Catholic Charities. This was a random act of violence.
A gunman with an apparent dislike of white people and government killed three people in downtown Fresno, California, on Tuesday, before he was taken into custody while shouting "Allahu Akhbar", police said. Police suspect that the man responsible for three shooting.
Kori Ali Muhammad is in custody and is expected to be charged with four counts of murder.