Detectives investigating Saturday evening's attack inside the South Bay Galleria in Redondo Beach said they don't have a motive.
The boy and girl suddenly collapsed outside the mall's movie theaters after being stabbed in the chest.
Police Sgt. Shawn Freeman said they were hospitalized in stable condition Sunday after undergoing surgery.
Freeman said no one saw the stabbing, and there was no screams or shouts from the victims or witnesses. Before the boy passed out, he provided a general description of a suspect.
Investigators were reviewing surveillance video to help them identify the man.
Information from: Daily Breeze, http://www.dailybreeze.com