The threat was also made to New York City — which dismissed the warning as an amateurish hoax.
But in an extremely rare move, Los Angeles reacted by shutting down the entire school district, reflecting the lingering unease in southern California following the terrorist attack that killed 14 people at an office lunch two weeks ago in San Bernardino.
In LA, the threat came in the form of an email to a school board member.
Authorities in New York reported receiving the same “generic” email but decided there was no danger to schoolchildren, with mayor Bill de Blasio concluding that the threat contained “nothing credible”.
“It was so outlandish,” he said.
New York police commissioner William Bratton agreed, quipping that it looked like the sender of the threat had watched a lot of the Showtime cable TV terrorism drama Homeland.
Mr Bratton, who once ran the LA Police Department, called the closure in Los Angeles a “significant over-reaction”.
“We cannot allow ourselves to raise levels of fear,” he said.
The LA shutdown abruptly closed more than 900 public schools and 187 charter schools attended by 640,000 youngsters across the city. More than 1,500 buildings were searched.
LA officials defended the move, with the city’s police chief condemning the criticism as “irresponsible”.
“It is very easy in hindsight to criticise a decision based on results the decider could never have known,” Charlie Beck said.
Southern California, he said, “has been through a lot in the recent weeks. Should we risk putting our children through the same?”.
The city later announced that schools would reopen yesterday, with increased police patrols outside campuses. Mayor Eric Garcetti said the FBI had concluded that the threat was not credible.