"In order to avoid further provocations, we pulled out from the border, even the tactical units which had been there for training purposes," Deputy Defence Minister Anatoly Antonov said.
His remarks came a day after President Vladimir Putin said Russia had withdrawn its troops, a claim rejected later in the day by the Pentagon and the White House, Xinhua reported.
So far, no NATO country has formally submitted any complaint over Russia's alleged violation of its international obligations concerning conventional weapons, Antonov said.
The official said Ukraine had deployed 15,000 troops near the border with Russia and that Kiev had resumed the military draft, adding that it coincided with a NATO military build-up in Eastern Europe.
"Such actions do not facilitate de-escalation of tension in Ukraine," Antonov said.