Putin, who heads to China for economic and political talks this week, said spring military drills in the Rostov, Belgorod and Bryansk regions had been completed and that troops were to return to their normal bases, the Interfax news agency reported without further detail.
Russian officials had said two weeks ago that their forces were withdrawing from the 1,000-mile border with Ukraine, although
Top NATO officials said last month that satellite surveillance showed the Kremlin had amassed at least 40,000 soldiers on Ukraine's border.
Ukrainians are set go to the polls on Sunday to elect a new president to replace ousted former leader
It wasn't clear if the troop withdrawal order was a further signal that the Kremlin will let Sunday's election take place without interference. Armed pro-Russia separatists have occupied government buildings in the Donetsk and Luhansk regions over the last two months and vowed to prevent the Kiev-administered election from taking place in the areas they control.
The separatists, who have barricaded themselves in seized government buildings, organized their own vote on May 11, after which they declared independence from Ukraine. Some self-styled leaders of the breakaway areas have appealed to Russia for
Ukraine's embattled interim leaders, who took power after Yanukovich fled, have accused Putin of orchestrating the violent takeovers in eastern Ukraine, and U.S. and European governments have also blamed the Kremlin.