The Russian defence ministry on Monday said it was pulling back a battalion from a region on the border with Ukraine but it was not clear if this was linked to a wider troop movement to defuse tensions.
A battalion from the central military district's 15th motorised infantry brigade finished manoeuvres at the Kadamovsky range in the Rostov region bordering Ukraine and would now return to its home region of Samara on the Volga, the defence ministry said in a statement to Russian news agencies.
There was no information on the number of troops involved. A battalion normally comprises no more than around 1,000 troops. Ukraine and the United States have accused Russia of massing tens of thousands of troops on the eastern Ukrainian border.
A Ukrainian defence ministry official had told AFP in Kiev earlier Monday that Russian forces have began a gradual withdrawal from the Ukrainian border.
US Secretary of State John Kerry met Russian Foreign Minister Sergei Lavrov in Paris on Sunday for talks that reached no breakthrough on the crisis but ended with an agreement for the sides to resume negotiations soon.