President Vladimir Putin has ordered Russian troops on military exercises near the Ukraine border to return to their bases.
The Kremlin announced on Monday the three regions involved are Rostov, Belgorod and Bryansk. Defence officials have insisted the troops were involved in regular training.
Russia has made similar statements in the past. But NATO Secretary-General Anders Fogh Rasmussen said there was no evidence of any withdrawal so far.
Correspondents say removing the troops - estimated to number 40,000 - could help de-escalate the Ukraine crisis.
The BBC reports tensions between Russia and the West rose after the overthrow of President Viktor Yanukovych in February, following months of street protests in Kiev and other cities.
Ukraine is preparing for presidential elections on 25 May.
On Monday, Russian Foreign Minister Sergei Lavrov said Moscow's ties with the EU and NATO needed a "substantial rethink" in light of deep differences over Ukraine, Russian news agencies report.
Russia annexed Crimea after a referendum there on 16 March.