One of them is a 16-year-old boy, who was charged Friday as an adult and faces one count of murder.
Abel Diaz was being held in Los Angeles County jail; his bail is $1 million.
The other suspects arrested Thursday are a 21-year-old man and an 18-year-old man.
It appears Downey Officer Ricardo "Ricky" Galvez was shot Wednesday night during a botched robbery, Corina said.
Galvez had just returned to department headquarters from K-9 training after 11 p.m. and was sitting in a public parking lot not far from an entrance to the station. He had been in his car for a few minutes when two men approached.
Some of the suspects have admitted to the attempted robbery, Corina said. The men probably didn't realize Galvez, who was not in uniform, was a police officer, he said.
An officer in a patrol car heard gunfire and saw two men get into another vehicle and race off, Corina said. That officer chased the car to the nearby community of Montebello, where the three suspects bailed out, Corina said. The driver was caught soon after he tried to flee.
Investigators have taken a revolver into evidence, officials said.
Officer was driving his own vehicle
Galvez worked five years for police in Downey, a city of roughly 114,000 people about 10 miles southeast of downtown Los Angeles.
He served in the Marines and spent tours in Afghanistan and Iraq.
"Ricky was an outstanding person, outstanding police officer," said Lt. Mark McDaniel of the Downey Police Department. "If you could mold a police officer, you would mold that police officer after Ricky Galvez."
McDaniel said Galvez loved serving his city and his country.
"Ricky ... was a tremendous young man who loved serving the residents of Downey," Charles said. "His smile was infectious and his professionalism was always on display."
"Our department is hurting," the chief said, "and I would ask that everyone keep Ricky's family and members of this department in your prayers."