Gov. Gavin Newsom called on Tuesday for a statewide ban on smartphone use in California schools, joining a growing national effort to curb cyberbullying and classroom distraction by limiting access to the devices.

Mr. Newsom, who has four school-age children, said he would work this summer with state lawmakers to dramatically restrict phone use during the school day in the nation’s most populous state. His directive came hours before board members at the Los Angeles Unified School District,…