Lufthansa and its subsidiary Austrian Airlines are the only two Western carriers flying into Tehran, which is mostly served by Turkish and Middle Eastern airlines.
The region and the United States have been on alert for an attack by Iran since April 1, when Israeli warplanes are suspected to have bombed the Iranian embassy compound in Syria.
German Foreign Minister Annalena Baerbock called her Iranian counterpart Hossein Amirabdollahian to call for "maximum restraint" on all sides and avoiding further escalation.
Lufthansa said it had suspended flights to and from Tehran until probably April 13, extending its suspension by two days, to avoid its crew having to disembark to spend the night in the Iranian capital.
"Last weekend it was decided not to operate a flight to Tehran with a layover for the crew due to the security situation," a spokesperson said. "On the route, the crew has to spend the night in Tehran before the return flight to Frankfurt. We want to avoid disembarking for safety reasons."
Austrian Airlines, which is owned by Lufthansa and flies from Vienna to Tehran six times a week, said it was still planning to fly on Thursday but was adjusting timings to avoid an overnight layover.
"The Austrian Airlines flight to Tehran scheduled for today will take place, but will depart from Vienna several hours late in order to minimise the time between landing and departure in Tehran," a spokesperson said.
Iranian air space is also a key overflight route for Emirates' and Qatar Airways' flights to Europe and North America.
Emirates, Qatar Airways, Turkish Airlines, Aeroflot and Air Arabia, among the airlines which fly to Tehran, did not immediately respond to requests for comment.
Flydubai said its flights to Iran are still currently scheduled to operate.
Businesses in Qatar, United Arab Emirates and Turkey were closed for the Muslim Eid al-Fitr holiday.
"Avoiding further regional escalation must be in everyone’s interest. We urge all actors in the region to act responsibly and exercise maximum restraint," the German foreign ministry said in a post on X.
