Numerous Russians have rushed to reserve one-way tickets out of the country after President Vladimir Putin decreed a partial mobilization of military reservists for the war in Ukraine.
Russian Defense Minister Sergei Shoigu said in a televised interview that 300,000 reservists with relevant combat and service experience would initially be mobilized.
Ticket prices skyrocketed amid apparent fears that Russia's borders could soon close or that Putin might announce a general mobilization.
Large numbers of Russians have already left the country since Putin ordered his troops to invade Ukraine almost seven months ago.
Air Serbia, the only European carrier besides Turkish Airlines to maintain flights to Russia despite a European Union flight embargo, saw tickets for the Moscow-Belgrade flight quickly sell out for the next several days, while the price for flights from Moscow to Istanbul or Dubai reached as much as 9,200 euros ($9,119) for a one-way, economy-class fare.
A Belgrade-based group called Russians, Belarusians, Ukrainians, and Serbs Together Against War tweeted that there were no available flights to Belgrade from Russia until mid-October. It said flights to Turkey, Georgia, and Armenia also sold out.
Russians can enter Serbia without a visa. Belgrade has not joined Western sanctions against Russia for its aggression in Ukraine.
Allies such as Belarus and China also have not imposed sanctions on Russia.
Some social media postings alleged people already had been turned back from Russia's land border with Georgia and that the website of the state Russian railway company had collapsed because too many people were checking for ways out of the country.