The FBI said authorities believed the threats were not credible but US Representative Peter King said there would be an investigation, and officials were likely to look into whether ISIS was involved.
All the flights landed safely and no bombs or other hazardous materials were found after the inspection.
The threats were phoned in anonymously by the same person, according to the reports, which quoted an FBI statement.
US fighter jets were sent to escort one of the flights that had been threatened, an Air France flight from Paris to New York City.
A Delta Air Lines flight from Paris to Boston and United Airlines flights from Madrid and Edinburgh to Newark, New Jersey, were among the other flights affected.
The exact number of flights threatened wasn't clear. Some reports said the caller threatened four flights; others said as many as 10 were named.
US Representative Peter King said "I'm not saying ISIS is behind this, but it certainly is something that has to be looked into," King told CNN.
King said last week there had been "chatter" on Twitter about using hoaxes to cause chaos in the United States. The goal might have been to see how the US reacts.