The move comes shortly after the US and UK warned that Moscow could attack Ukraine at any time.
It is not clear how many military units will be withdrawn and it is not clear where they will be moved.
Some Russian units have withdrawn to their bases after the end of the drills near the border with Ukraine.
Ukraine and Britain have cautious reactions after Russia “retreats”.
But the move prompted a strong rally in financial markets.
Western military analysts say it is still too early to be certain that the conflict has eased.
Kremlin spokesman Dmitry Peskov said: “We have always said that our troops will return to their bases after the exercises are over. And it’s the same this time.”
In addition, Dmitry Peskov also accused the US of contributing to a crisis by repeatedly raising alarms about an impending attack.
After it was reported that Russia would withdraw some units from the border, the office of Ukrainian President Volodymyr Zelenskiy commented that this sent “the right signal”, Ukraine’s Liga news agency reported.
Meanwhile, NATO Secretary General Jens Stoltenberg said he saw hope for diplomacy to help end the confrontation between Russia and the West.