KIEV, Ukraine — The airport in the regional capital of Simferopol was closed on Tuesday to all flights except those heading to and from Moscow, in the boldest display yet of Russia’s tightening control over Crimea.

The announcement that air links had been severed between Crimea and the Ukrainian capital of Kiev raised the possibility that the peninsula might be closed off indefinitely from the rest of Ukraine, and it immediately prompted a sellout of tickets for connecting flights on Aeroflot, the Russian national carrier.

Even as Russia consolidated its grip on the embattled peninsula, diplomatic efforts between the Obama administration and the Kremlin appeared stalled, with the two sides continuing to engage in menacing military exercises and trade threats of economic retaliation.

Secretary of State John Kerry spoke by telephone on Tuesday with the Russian foreign minister, Sergey V. Lavrov, as they have repeatedly done since the outset of the crisis in Crimea, but neither side reported any substantial progress.