The defence ministry said that large-scale drills continued but that some units were returning to their bases.
There has been no independent confirmation of the withdrawal and international powers have reacted cautiously to the announcement.
More than 100,000 Russian troops have massed at Ukraine's border. Russia has always denied it is planning an attack.
Russia has deep cultural and historic ties with Ukraine, and has been seeking guarantees it will not join the Nato military alliance, something the bloc has refused to promise.
Troops began gathering in large numbers last November, bringing increasingly dire warnings about Russia's intentions. In recent days the US warned an invasion could be imminent, and moved its embassy out of the capital Kyiv.
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