Russian troops ordered by President Vladimir Putin to return to their bases from near the Ukrainian border were preparing their departure on Tuesday, the defence ministry said.
"The commanders in the exercise areas are now clarifying the routes and movement plans" for the troops to leave, Interfax quoted a ministry source as saying.
"The men have started dismantling their tent camps, loading equipment and forming columns of vehicles and armour," the ministry said.
Putin on Monday announced that the troops, estimated by NATO to number 40,000, were to return to bases after the end of spring exercises.
Their presence had raised deep concerns in the West after Moscow's annexation of Crimea in March and rebel uprisings in eastern Ukraine against the pro-Western authorities who took power in February following the the ouster of a Kremlin-backed government.
The withdrawal could ease tensions ahead of a presidential vote in Ukraine on Sunday, but both Washington and NATO -- which noted it was the third time Moscow had made such a claim -- have said they saw no sign of a pullback.