Russian President Vladimir Putin ordered all troops stationed along the border with Ukraine to withdraw, the Kremlin said on Monday.
Moscow had previously issued such orders, but NATO said the withdrawals have not happened.
The Kremlin said spring training had been completed in the Rostov, Belgorod and Bryansk regions and the units would return to their barracks.
Ukraine and the West have claimed that Russia has been massing tens of thousands of soldiers along the border, raising fears of an invasion in Kiev and prompting accusations from the West that the troops would further destabilise Ukraine, as its pro-Western government faces unrest from pro-Russian separatists.
Russia has justified the presence of the troops as part of maintaining Russia’s and the Russian people’s own security.
The Kremlin statement was issued as Ukraine heads into presidential elections this weekend. A separatist leader in the east vowed on Monday to ignore it and demanded the resignation of the current government in Kiev.
“We believe that the May 25 presidential election is not legitimate,” Pavel Gubarev, the self-declared “people’s governor” of Donetsk, told Rossia 24. “Naturally, we won’t recognise this election.”
Mr. Gubarev said it was illegal to carry out elections in the territory of the Donetsk People’s Republic and the neighbouring Luhansk People’s Republic and he doubts that the vote will take place.
Separatist leaders in those regions declared independence from Ukraine after holding referendums on May 11, which Ukraine and the West called illegal.