Lufthansa said it would also avoid using Iranian and Iraqi airspace until August 21, an extension from a previous date of August 13.
Affected passengers can rebook or cancel their journeys free of charge, Lufthansa said, adding that it regretted the inconvenience caused "due to the current situation".
Also on Monday, Air France and its subsidiary Transavia France again extended the suspension of their flights to Beirut, through Wednesday August 14.
The flights have been suspended since July 29 and their resumption "will be subject to a new assessment of the situation on the ground", Air France said in a statement. The French carrier continues to serve Tel Aviv's airport.
Other airlines have also modified their flight schedules in the region recently.
Tensions have soared as Iran and its allies vowed revenge for the high-profile killings of Hezbollah's top military commander Fuad Shukr in Lebanon and Hamas political leader Ismail Haniyeh in Iran late last month, both blamed on Israel.

Hezbollah has been exchanging near-daily fire with Israeli forces across the border between Lebanon and Israel.
This comes as leaders of France, Germany and Britain said Monday that "there can be no further delay" in negotiating a ceasefire in Gaza, warning Iran and its allies against any "further escalation" of the conflict.
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The joint statement came after one of the deadliest reported Israeli strikes on the besieged Gaza Strip in more than 10 months of war.
"The fighting must end now, and all hostages still detained by Hamas must be released," French President Emmanuel Macron, German Chancellor Olaf Scholz and British Prime Minister Keir Starmer said in a joint statement.
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