Israeli airspace was closed on 13 June after it launched its operation against Iran, prompting retaliatory strikes.
The FCDO said further flights would be considered depending both on demand and the latest security situation.
It added the volatility of the situation meant the ability to run flights “could change at short notice”.
British nationals and non-British immediate family members travelling with them are eligible for a seat, but places on the flight from Tel Aviv will be allocated according to need.
On X, the FCDO said the flight would be for “vulnerable British nationals and their dependents”.
Passengers will need the necessary travel documents and visas.
