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The Kremlin said a number of soldiers are returning to their permanent bases after finishing military drills. Western countries have accused Russia of amassing around 100,000 troops near Ukraine.
Russia announced on Saturday that 10,000 troops had finished month-long military drills near Ukraine and would be returning to their permanent bases.
The news comes amid accusations from Western countries that Russia is plotting an invasion of Ukraine, something the Kremlin denies.
The Russian Defense Ministry said in a statement that the operations for the Southern Military District forces had taken place across a stream of southern regions, including Rostov, Krasnodar and Crimea, a peninsula Moscow seized from Ukraine in 2014.
The West has accused Russia of amassing some 100,000 troops near its border with Ukraine.
In the meantime, Russia has applied pressure on NATO and the West with a raft of demands, calling for a Russian veto on the admission of future NATO members, with one eye on Ukraine's possible entry to the military alliance.
The United States, among others, have given the Kremlin's request short shrift.
In addition, Russia has called on NATO to withdraw its multinational battalions from Poland and the Baltic states of Estonia, Latvia and Lithuania.
President Vladimir Putin fanned the flames on Wednesday when he said Russia would take "appropriate retaliatory" steps in response to what he called an "aggressive stance" from the West.
But he turned the volume down the following day when he said he had witnessed a "positive" reaction from Washington to Russia's security proposals.
Talks between the US and Russia, as well as NATO, are scheduled to take place next month.
A senior US official said Washington was "ready to engage in diplomacy as soon as early January," both bilaterally and through "multiple channels."
Talks involving Germany, France and Ukraine under the Normandy Format in the new year have been hinted at.
jsi/rs (AFP, dpa)