A posting on Monday says, "My kill rate increases tremendously on the other side".
Muhammad was arrested shortly after the rampage.
The Federal Bureau of Prisons says Muhammad was incarcerated at a federal penitentiary from October 2006 to September 2011 after being convicted of possessing cocaine with intent to distribute.
But the shooter didn't want to go down in history for just one slaying, police said.
Muhammad also shot Mark Gassett, 37, of Fresno, who had just picked up groceries at a Catholic Charities building.
The two were waiting for the bus when authorities say Kori Ali Muhammad, who is black, targeted the white men at random. Greer said he ran into the Catholic Charities building. On the first of every month, Greer said Jackson would treat him to a meal at Denny's restaurant where they both ordered the club sandwich.
She didn't name the victim, but said he had been carrying a bag of groceries, was known to be homeless and was shot at least three times in the torso.
"This is exclusively based on race", he said. Muhammad shot him in the chest, and fired twice more after he fell to make sure he was dead.
He then set his sights on three white men standing at a bus stop.
David Jackson, 58, died at the scene.
Dyer said he doesn't think the suspect's desire to kill stemmed from religious views, but rather racist views.
Dyer described Muhammad as an extremely callous man.
Fresno police chief Jerry Dyer holds a news conference to go over details of Tuesday's triple homicide shooting in Fresno at the Fresno Police Department on Wednesday, April 19, 2017.
After Kori Ali Muhammad learned that he was wanted in the death of a security guard last week, he chose to take out as many other white men as possible before he was caught, Fresno Police Chief Jerry Dyer said.More news: Jackie Robinson Statue To Be Unveiled At Dodger Stadium
When arrested, he is said to have told officers: "I did it".
When Muhammad later saw a police vehicle, he surrendered. He also was wanted in connection with another killing days earlier, in which a security guard was gunned down at a Fresno motel after responding to a disturbance. He told investigators that he did not like white men and that "white people were responsible for keeping the black people down". Police said he hid out in a ravine after the motel shooting and practiced voodoo rituals.
"He said he is Muslim, but prays to seven different gods", the police chief said.
"During his arrest, Muhammad shouted "Allahu Akbar", but Fresno Police Chief Jerry Dyer said the shootings had "nothing to do with terrorism in spite of the statement he made".
"I did it. I shot them", Dyer said Muhammad told officers.
"What Kori (Muhammad) said was that he fired his weapon at Carl Williams because he felt that Carl Williams had disrespected him", Dyer said.
Police had been looking for Muhammad in the death of the guard, 25-year-old Carl Williams. Police say Williams was unarmed.
"The diocese will be present to the needs of all those serving as witnesses to this violent and traumatic event", she told the newspaper, "such as counseling and pastoral care, and Bishop Ochoa asks for the prayer of all the faithful for the victims of this violent crime and their families, and that law enforcement will be successful in the their investigation in identifying the perpetrator".
Randalls was married for eight years to a local elementary school teacher and they had two kids, a 4-year-old boy and 3-year-old girl.
The last victim, 58, was gunned down in the vehicle park of a charity building.
Prosecutors plan to review the case against Muhammad on Thursday and he could be arraigned in court on Friday.
Meanwhile, family and friends mourned the four men. The gunman pumped two more rounds into Gassett as he lay on the ground, police said.
Eddie Valencia said Wednesday that he and Zackary Randalls were friends for 15 years after bonding on a job over a love of music and the Los Angeles Dodgers.
Randalls was in a training program for Pacific Gas & Electric and doing a ride-along Tuesday when he was gunned down. The driver was not hit and sped toward the police department, but his partner could not be saved.