Russia has started making combat readiness inspections in its southern military district, which borders Ukraine, involving more than 6,000 troops, the RIA news agency cited Russia's military as saying on Tuesday.

The Kremlin earlier said it was watching with great concern after the United States put 8,500 troops on alert to be ready to deploy to Europe in case of an escalation in the Ukraine crisis.

On Sunday and Monday, the U.S. and the United Kingdom governments decided to evacuate their embassy staff and their families from Kyiv.

NATO allies are sending more ships and jets to "enhance deterrence and defense" in eastern Europe as Russia "continues its military buildup in and around Ukraine," the organization announced on Monday.

Along with its European allies, the U.S. warned that Russia is setting the stage to invade Ukraine and has deployed over 100,000 troops on its border with the former Soviet republic alongside heavy artillery and tanks.