Aeroflot, Russia's state airline, said on Saturday that it would suspend all international flights from Tuesday due to additional circumstances that prevent the performance of flights.
Aeroflot said it would continue to fly to Minsk, the capital of Belarus, despite the cancellation.
Russia's airline industry has been hit hard because of sanctions imposed on Russia by other countries. Russian forces have attacked Ukraine from Belarus, and are allies of Mr. Putin and President Lukashenko.
Russia's aviation authority recommended on Saturday that Russian airlines with planes registered in foreign countries stop all flights from Sunday because of fears that they could be seized.
Russian airlines will no longer be able to fly foreign-made aircraft on international routes because of the suspension.
It is likely to become harder for Russian airlines to use foreign-made aircraft because of the suspension of parts, maintenance and technical support services by companies such as Boeing and Airbus.
There were 332 Boeing aircraft in the Russian airline fleet as of the beginning of March, according to a report.
The European Union has ordered the end of aircraft leases by Russian companies. Russia banned Western-based airlines from entering its airspace.