Russia's defence ministry said on Friday it had begun returning troops and military units from annexed Crimea to their permanent bases following a huge build-up near Ukraine's border that had raised concerns in Kyiv and the West about the risk of war.
Russia announced on Thursday it had completed a "snap inspection" of military drills in its south and west after weeks of tensions with the West over its concentration of tens of thousands of troops near Ukraine.
Ukraine gave a guarded welcome to the troop drawdown.
"If Russia really pulls back from the border with Ukraine the enormous military force it has deployed there, this will already ease tensions," Foreign Minister Dmytro Kuleba said in a statement.
"But we need to remember that this step would put an end neither to the current escalation, nor to the conflict between Ukraine and Russia in general."
Washington has said it is waiting to see what actions follow Moscow's announcement and it will "continue to watch very closely".
Russia on Friday said troops from its southern military district and airborne troops that took part in the snap inspection were beginning to rebase.
It said that military units and formations were marching to railway loading stations and airfields and aired footage of armoured vehicles boarding landing ships on a beach and other military vehicles being loaded onto trains. Soldiers were shown marching onto a military aircraft.
A confirmed pullout of the troops brought in on top of the permanent contingent will likely be welcomed by Western countries which had been expressing alarm at the prospect of further potential Russian intervention in eastern Ukraine. Russian-backed separatists have been fighting the Ukrainian government in the region since 2014.
Moscow and Washington are at odds over an array of disagreements. Former prime minister Dmitry Medvedev, a close ally of President Vladimir Putin, said on Friday that relations had essentially returned to the Cold War era.
Washington imposed sanctions on Moscow and expelled diplomats last week, but President Joe Biden has also proposed he and Putin meet for a summit. The Kremlin has not yet said whether or not Putin will accept. On Friday, the Kremlin said the troop pullback had nothing to do with ties with Washington or a possible Biden-Putin summit and blamed the United States for the dire state of relations, saying that Moscow wanted to revive bilateral ties.