The Russian Defense Ministry says its units in the western regions bordering Ukraine are preparing for a journey to their home bases in line with President Vladimir Putin's order.
Putin ordered the withdrawal yesterday in what could be an attempt to ease tensions with the West over Ukraine.
Putin's order appears to go further than his claim two weeks ago that troops were being pulled back from the border to shooting ranges.
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The US and NATO, which estimates that Russia has 40,000 troops along the border with Ukraine, said they saw no immediate sign of a pullout after Putin's claim.
The Defense Ministry today said that its forces in the Bryansk, Belgorod and Rostov regions are dismantling their summer camps in preparation for a march to their home bases.