American Airlines not ready to resume Israel flights

Still assessing FAA ban: American Airlines CEO

American Airlines is not ready to resume flights to Israel, even though the FAA has lifted the ban, CEO Doug Parker told CNBC on Thursday.

"The ban was just lifted," Parker said in a "Squawk Box" interview. "We need to access that."

He said he's hopeful service will resume by the airline's next scheduled flight to Tel Aviv, late Thursday from Philadelphia, "but we have to make sure, as all airlines do, that conditions are indeed stable,"

"The FAA lifting the ban is a necessary, but not a sufficient, condition," Parker said, while pointing out that American Airlines canceled flights before the FAA put in place the ban.

The FAA imposed the ban Tuesday after a Hamas rocket landed near Israel's Ben Gurion International Airport.

Read MoreFlightban to Israel lifted, Gaza toll tops 700

"The conditions that allowed them to lift the ban has given us some encouragement," Parker said. "But we need to make sure our people have the same view. We have pilots and flight attendants that are going to be flying that route that need to be certain of the same things."

The bottom line, he said, "We are not going to fly the flight unless we're absolutely, positively certain it's safe. We're hopeful that will be the case. but we have not reached that conclusion yet."

—By CNBC's Matthew J. Belvedere