LOS ANGELES—Two men were charged with murder Thursday for a road-rage crash that killed a 5-year-old boy and critically injured the child’s mother and his infant sister, authorities said.

Brian Barnes, 44, and Armando Gamboa Ayon, 19, both of Los Angeles, each face one count of murder, vehicular manslaughter and three counts of reckless driving causing specified injury. Barnes also was charged with three counts of leaving the scene of an accident.

Both men were booked on more than $1 million bail. Both men appeared in court Thursday but their arraignment was delayed until Oct. 17.

“We’re going to throw the book at them and enforce the law, because what happened to that family was unacceptable,” Mayor Antonio Villaraigosa said at a news conference.

Police said the two men were driving their cars Tuesday in the San Fernando Valley when they got into an argument. The vehicles weaved along city streets between speeds of 50 mph to 90 mph, “cutting each other off” and jockeying for position, said Detective Bill Butos said.

Police said one the drivers was tapping on his brakes, trying to get the other motorist to ran into his vehicle.

Barnes eventually slammed on his brakes and Ayon tried to avoid the vehicle and plowed into the back of a parked car, Officer Jason Lee said. The parked car slammed into another vehicle, crushing the boy, Ayman Arif, his sister, Ikra Arif, and his 31-year-old mother Syeda Arif.

All three were taken to the hospital where Ayman was taken off of life support late Wednesday, police said. Syeda Arif and her daughter were both listed in critical condition.

Ayon was arrested at the crash site and Barnes later surrendered at a police station after he drove away from the scene.

Outside court, Barnes’ aunt, Carol Uri, sent along prayers to the Arif family and an attorney for Ayon apologized on behalf of his client’s family to the victims.

“They want to say how really sorry they are for everything that happened,” said Ayon’s attorney Howard Levine.