Four of the children were in critical condition when firefighters arrived but they were stabilised and were in serious condition at a hospital, city fire Captain Jaime Moore said. Everyone was expected to survive, he said.
The powder blue Cadillac backed slowly into the group of parents and children buying snacks from a sidewalk vendor, and the crowd banged on his windows and screamed for him to stop, but not before some of the children were trapped under the car, witnesses said.
Children's backpacks, shoes, candy and loose change were strewn about the scene behind a discount grocery store across from Main Street Elementary.
Police identified the driver as Preston Carter and said he was being very cooperative.
Carter talked to television reporters after the crash some five miles southwest of downtown Los Angeles. He said he has a driver's license and will be 101 years old Sept. 5.
"My brakes failed. It was out of control," Carter told KCAL-TV.
Asked about hitting the children, Preston said: "You know I'm sorry about that. I wouldn't do that for nothing on earth. My sympathies for them."
Carter was pulling out of the grocery store parking lot, but instead of backing into the street, he backed onto the sidewalk, police Captain George Rodriguez said.
"I think it was a miscalculation on his part. The gentleman is elderly," Rodriguez said. "Obviously he is going to have some impairment on his decision making."
Older drivers have been involved in other tragedies. In 2003, an 86-year-old man mistakenly stepped on the gas pedal of his car instead of the brake and then panicked, plowing into an open-air market in Santa Monica. Ten people were killed and 63 injured.
According to California's Department of Motor Vehicles, people over age 70 must renew their driver's license in person, rather than via the Internet or by mail. Older drivers can also be required to take a supplemental driving test if they fail a vision exam, or if a police officer, a physician, or a family member raises questions about their ability to drive.
Rodriguez said the collision was being investigated as an accident, and Carter was not under arrest. He has a valid driver's license, Rodriguez said.