The ban, which was ordered Tuesday morning, came after a rocket struck about a mile from the airport in Tel Aviv.
The ban is applicable only to U.S. carriers, although many other airlines also terminated service to Tel Aviv on Tuesday.
"The agency is working closely with the government of Israel to review the significant new information they have provided and determine whether potential risks to U.S. civil aviation are mitigated so the agency can resolve concerns as quickly as possible," an FAA statement said Wednesday.
At a press briefing Wednesday, the State Department confirmed that rockets had landed near the Tel Aviv airport. Spokesmen said they were still determining whether Hamas, the militant group that rules the Gaza Strip, possesses heat-seeking antiaircraft missiles such as the that downed a Malaysia Airlines flight over eastern Ukraine.