(CNN) A black man accused of fatally shooting three white men in what police are calling a hate crime said that he "snapped" after thinking "about all the injustice and the atrocities that my people go through."

Kori Ali Muhammad, 39, allegedly shot at the men at random in downtown Fresno, California on April 18. At the time, Muhammad was already wanted by police in the fatal shooting of Carl Williams, a 25-year-old unarmed security guard, on April 13, police said.

Muhammad admitted to the shootings in a recent jailhouse interview with CNN affiliate KGPE that appears to give more insight into his state of mind and motives.

"Someone has to fight for all the people who died at the hands of racist white men," he told the news station on Saturday.

"I was actually going to go turn myself in, and then I started thinking about the missing black women and children," he said. "I started thinking about Flint, Michigan. I started thinking about the crack cocaine epidemic. I started thinking about all the injustice and the atrocities that my people go through. And that's why I snapped."

"I wasn't thinking like ... I'm going to kill, kill, kill. All I knew was white supremacy has to die and the people who benefit from white supremacy ... are white men," Muhammad said.

Muhammad will now face four counts of murder -- one in Williams' death and three in the shooting rampage - and two counts of assault with a deadly weapon, officials said. Muhammad's attorney did not immediately return a request for comment.

His arraignment in Williams' death, which was scheduled for Monday, was suspended pending a mental competency evaluation. His next court date is May 12, 2017, according to Steve Wright, assistant district attorney for Fresno County.

The FBI is assisting Fresno police in the investigation.

Suspect: Someone has to fight for deaths by 'racist white men'

Last week, Fresno Police Chief Jerry Dyer said Muhammad had previously posted on social media about his dislike for white people and government officials. He also yelled "Allahu Akbar" (God is greatest) when he was arrested shortly after the shooting, officials said.

"We do not believe ... that this is a terrorist-related crime," Dyer told reporters then. "This is solely based on race."

Police said Muhammad shot the three white men, firing 16 rounds in 60 to 90 seconds within a block and a half in the downtown area.

Zackary Randalls, a 34-year-old worker for the Pacific Gas & Electric utility, was killed, along with Mark Gassett, 37, and David Martin Jackson, 58.

Gassett and Jackson were standing near Catholic Charities, a social services agency where they are clients, police said.

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.

Authorities said Muhammad also 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 car, which they had trouble starting.

Dyer said Muhammad approached the passenger side and pointed the gun at them but didn't fire.

"That's the only regret I have, because in the car was a woman and children. I am glad none of them got hit," Muhammad said in the jailhouse interview. "I probably couldn't live with myself if I hit the woman and child. I had no intentions of hurting women and children."

Suspect: I shot security guard over disrespect

At the time of the shooting, police were looking for Muhammad in connection with Williams' death outside a Fresno motel.

In the interview with KGPE, Muhammad said the security guard was arguing with a friend of his and "being very disrespectful, so I shot him."

"You shot the security guard?" Reporter Matt Mendes asked,

"Yes, sir," Muhammad said.

He also said he hid from police on the roof of a 7-11.

"I scaled the wall, got on top of the roof, stayed there until I felt it was safe enough to get down," Muhammad said, according to the station.

Days later, Muhammad said he discovered he was wanted by police, who had circulated his photo and asked for the public's help in apprehending him.

His previous run-ins with the law include a 2005 indictment on charges of cocaine possession with intent to distribute, and possession of two rifles and a semi-automatic handgun, court records show.

Muhammad's public defender had raised questions about whether he was mentally fit to stand trial, noting that on several occasions he had "appeared eccentric with some bizarre beliefs" and appeared to have hallucinations. The lawyer also said his client had "at least two prior mental health hospitalizations."

A psychiatric evaluation later found Muhammad suffered from psychosis and a substantial degree of paranoia. He was declared not competent to stand trial in July 2005.

He was later found competent for trial in 2006 after a previous order had committed him to a facility.

Muhammad pleaded guilty and was sentenced to 110 months in prison, which was reduced to 92 months.