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The United States on Sunday asked its citizens in Russia to "consider" leaving immediately, as commercial airlines cancelled flights and nations shut airspace in efforts to tighten the screws on Moscow for invading Ukraine.

"An increasing number of airlines are cancelling flights into and out of Russia, and numerous countries have closed their airspace to Russian airlines," said the US embassy in Moscow in a statement.

It called on its citizens to "consider departing Russia immediately via commercial options still available."

But the US embassy said that Washington was not changing its travel advisory to Russia.

It implemented a Level 4 "Do Not Travel" warning against Russia in January, as tensions over Ukraine grew.

Earlier Sunday the European Union, outraged at Russian President Vladimir Putin's deadly assault on Ukraine, closed its airspace to Russian aircraft.

The measure consolidated what was already de facto largely in place, with many of the EU's 27 member nations having individually announced airspace closures to Russian flights.

Canada and Britain have also closed their airspace. 

In tit-for-tat punitive measures, Russia has also been closing its airspace to various European carriers.

Meanwhile Russian carrier Aeroflot said on Sunday it was suspending all flights to Europe.