Islamic State sympathizers may have been behind more than a dozen threats in the last two days to international flights using U.S. airports or flying over American airspace, U.S. law enforcement and security sources said on Wednesday.

The sources, speaking on condition of anonymity, said that after 11 threats were received by U.S. law enforcement officers on Monday, at least four more were phoned in late on Tuesday.

The threats were all similar and the caller claimed the flights were carrying some form of chemical weapons, they said, adding that investigators' leading theory was that sympathizers of Islamic State were responsible.

The Islamic State group declared a caliphate in parts of Syria and Iraq and established a presence in Libya, Afghanistan and other places with weakened central governments.

English language messages published on Twitter have said if supporters did not have weapons they should make their own or take whatever action they can to disrupt western societies.

At least one of the four flights threatened on Tuesday was out of Los Angeles, the sources said. They did not give details of the other flights.

They said all the threats on Monday appeared to have come from the same individual. One flight, Air France flight 22 from Paris, was escorted by two U.S. F-15 fighter jets to New York's John F. Kennedy International Airport.

The plane landed safely and was cleared with no incidents or hazards reported by passengers or crew, said J. Peter Donald, an FBI spokesman.

Threats were also made on Monday to flights both to and from other U.S. airports, including Newark and Atlanta, as well as flights between other foreign cities in Europe, North and South America and the Middle East, one official said.

No evidence of dangerous substances was found but officials said the threats were disruptive and wasted law enforcement resources.

U.S. aviation security authorities usually receive and investigate an average of one such threat per day, one of the officials said.