Some troops in Russia's military districts adjacent to Ukraine are returning to their bases after completing drills, Russia's defence ministry was quoted as saying on Tuesday.
Russia's Interfax news agency cited the ministry as saying that while large-scale drills across the country continued, some units of the Southern and Western military districts had completed their exercises and started returning to base.
The reported movements run counter to warnings from the United States and Britain that Russia may be poised to invade Ukraine at any time.
British Foreign Secretary Liz Truss said Britain would need to see a full-scale removal of Russian troops from the border with Ukraine to believe that Moscow has no plans for an invasion.
Video footage provided by the defence ministry and published by the RIA news agency showed some tanks and other armoured vehicles being loaded onto railway flatcars.
The ministry said it would use trucks to move some hardware while some troops would march to bases on their own.
Russia has amassed over 100,000 troops near Ukraine's borders, including a large contingent on joint drills in Belarus until February 20, meaning that Ukraine is almost encircled by the Russian military.
Russian markets reacted positively to the news and the rouble, which has been under pressure due to fears of fresh Western sanctions in the event of a war, gained 1.5% shortly after the defence ministry announcement.
Moscow has denied ever planning to attack Ukraine but is demanding legally binding guarantees from the United States and NATO that Kyiv will not be allowed to join the military bloc. Washington and Brussels have so far refused to make such pledges.
German Chancellor Olaf Scholz was expected in Moscow later on Tuesday to meet President Vladimir Putin in a high stakes mission to avert war.
