Russia announced Saturday that more than 10,000 troops had finished month-long drills near Ukraine, amid Western accusations that Moscow was plotting an invasion of its ex-Soviet neighbour.
The defence ministry said in a statement that the drills for Southern Military District forces had taken place in a host of southern regions including Rostov, Krasnodar and Crimea, which Moscow seized from Ukraine in 2014.
The defence ministry said the troops were returning to their permanent bases and that stand-by units would be readied for the New Year's holidays.
Western countries have accused Russia of massing upwards of 100,000 troops near Ukraine ahead of a possible winter invasion.
According to Kiev's estimates, the number of Russian troops along Ukraine's borders has increased from around 93,000 troops in October to 104,000 now.
Russia says it is free to move its forces on its territory how it sees fit and denies that it is planning a large-scale attack.
It has presented the West with sweeping security demands, saying NATO must not admit new members and seeking to bar the United States from establishing new bases in former Soviet republics.
Tensions reached a boiling point on Wednesday when President Vladimir Putin said Russia would take "appropriate retaliatory" military steps in response to what he called the West's "aggressive stance".
But he lowered the volume the next day, saying he had seen a "positive" reaction from the United States to Russia's security proposals and said talks would take place next month.
A senior US official has said Washington was "ready to engage in diplomacy as soon as early January", both bilaterally and through "multiple channels".
On Saturday, a German government official said Moscow and Berlin had agreed to a meeting in "early January".
German leader Olaf Scholz and Putin in a phone call Thursday agreed to the meeting between the chancellor's diplomatic adviser, Jens Ploetner, and the Kremlin's pointman on relations with Ukraine, Dmitry Kozak.
In an interview on Friday, a senior Ukrainian security official told AFP that there was no risk of an imminent Russian invasion.
Kiev has been battling pro-Russia separatists since shortly after Moscow annexed Crimea in 2014 in a conflict that has claimed over 13,000 lives.
The West has long accused the Kremlin of providing direct military support to pro-Russia separatists in eastern Ukraine. Russia denies the claims.