Those suspensions came on top of the previously announced cancellation of its flights to Tel Aviv in Israel.
"Air France will provide further information on its flight schedule to these destinations for the following days at a later date," the French flag carrier said in a statement.
Other European airlines cancelled dozens of services to and from the Middle East on Sunday, as Israel and Iran traded new attacks.
British Airways said it would not fly to Tel Aviv and Bahrain until March 4th, and cancelled flights to the Jordanian capital, Amman.
Swiss International Air Lines suspended flights to and from Tel Aviv until March 7th, and cancelled flights from Zurich to Dubai scheduled for Sunday.
Germany's Lufthansa, which includes Swiss and ITA Airways, cancelled its flights to and from Tel Aviv, Beirut, Amman, Erbil and Tehran until March 7th.
Flight tracking site FlightAware said that more than 6,700 flights had been delayed and 1900 cancelled globally as of 10am GMT on Sunday, on top of thousands the day before.
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