Russian President Vladimir Putin ordered troops near Ukraine's border taking part in military exercises to return to their permanent bases, the Kremlin said in a statement Monday, although NATO said so far it has seen no evidence of withdrawing troops.
Moscow has made similar statements before, leading NATO, Brussels and Washington to dispute that any withdrawals had taken place.
"In connection with the completion of the planned spring phase of training troops ... on the ground in Rostov, Belgorod and Bryansk regions ... the Russian President gave the command to the Minister of Defense to return the troops who took part in the exercises," the president's office said, in a statement posted on its website.
However, NATO's top official Anders Fogh Rasmussen said: "We haven't seen any evidence of Russian withdrawal of troops and I regret that."
Russia has about 40,000 troops deployed near the border with Ukraine.
On Friday, pro-Russian insurgents retreated from government buildings in the major eastern Ukrainian city of Mariupol as steelworkers began citizen patrols.
Ukraine is set to go the polls on May 25 to elect a new president. Recent polling cited by the Kiev Post newspaper indicates that businessman Petro Poroshenko, known locally as the "chocolate king" for his interests in the candy business, is the clear front runner.
Moscow has repeatedly said that the results of that election will be illegitimate.