Local media quoted police chief Jerry Dyer as saying Muhammad shouted "Allahu Akbar" as he was taken into police custody yesterday, the Los Angeles Times reported.
Dyer said all of Muhammad's victims Tuesday were white.
"These were unprovoked attacks by an individual that was intent on carrying out homicides today, and he did that", he said. After that, he encountered another man, who he shot and killed, Dyer said.
Dyer said that it's too soon to determine if the shootings involved terrorism.
Two shaken catholic charity workers ducked under yellow police tape to get out.
A former classmate of the man suspected of shooting three people to death in Fresno says that when they met he was outgoing, down to earth, peaceful and into health and nutrition.
The three people killed today were white men, as was the motel security guard, Dyer said.More news: Zimmermann sharp as Tigers beat Red Sox 4-1
Nine News also reported that although this is a domestic incident, global links to terrorism are also being investigated.
Kori Ali Muhammad, 39, was arrested shortly after the rampage.
Muhammad, who the police said had previous arrests for drug crimes and making a terroristic threat, indicated on Facebook that he had also spent time in Sacramento, where he said he attended high school. He was wanted before Tuesday's shooting spree in connection to a murder that happened last week at a nearby motel, where the victim was also white.
Authorities did not publicise his identity as they were chasing possible sightings of Muhammad and other leads in the case, Dyer said. He had been associated with gangs but was not a validated member.
County government buildings were placed on lockdown during the shooting spree and residents were urged to shelter in place. Also, Seyed Ali Ghazvini's first name was misspelled Sayed. In all, three people were killed in the incident.
He shot a 34-year-old PG&E truck passenger and two other men - a 37-year-old and a 58-year-old - in downtown Fresno, Dyer said. Muhammad continued on foot to Fulton Street where he shot and killed a white male.