An Airbus A-380 that departed from Los Angeles landed in Salt Lake City, where passengers and crew were being taken off the plane and escorted into the terminal, an FAA spokesman said.
A separate flight that left Dulles International Airport outside Washington, D.C., was diverted to Halifax International Airport in Nova Scotia, where passengers and crew had disembarked.
In a brief statement, Air France said both flights had been the "subjects of anonymous threats received after their respective take-offs."
"As a precautionary measure and to conduct all necessary security checks, Air France, applying the safety regulations in force, decided to request the landings of both aircraft," the airline said in its statement.
"Local authorities are carrying out complete inspections of the aircraft, their passengers and their luggage," the statement said. "An investigation will be led by the authorities to identify the source of the telephone call."
Security officials have been on high alert since last week's deadly attacks in Paris, claimed by Islamic State militants, killed 129 people, and after Russia said the group was responsible for the downing on Oct. 31 of a plane returning to St. Petersburg from the Sharm al-Sheikh resort in Egypt, killing all 224 on board.
Halifax airport spokesman Peter Spurway said the Air France Boeing 777 jet was diverted to Halifax at 10:15 p.m. eastern time and was currently parked at the end of the airport's main runway.
"It's an RCMP matter," Spurway said referring to the Royal Canadian Mounted Police. "The passengers are being deplaned at this point and being transferred to a secure area of the terminal building because they're international passengers."
CNN, citing a U.S. government official, reported that Flight 65, the flight originating in Los Angeles, was diverted after a bomb threat was called in from the ground. The official did not know if anyone was arrested in connection with that incident.
"Several law enforcement agencies are working in concert, following established protocol, to determine the nature of the threats which caused the aircraft to divert," FBI Special Agent Todd Palmer, of the agency's Salt Lake City division