Russian President Vladimir Putin has ordered troops staging military drills in areas near Ukraine to return to their home bases.
The Kremlin made the announcement Monday, just days before a crucial presidential election in Ukraine.
Western countries have protested the deployment of tens of thousands of Russian troops near the Ukraine border, expressing concern the deployment might be preparation for a land grab after Russia annexed Crimea in March.
NATO said Monday it has yet to see any sign of a withdrawal.
The Kremlin also called Monday for Kyiv to immediately withdraw its troops from eastern Ukraine.
The Ukrainian army and police have sought to put down a pro-Russian rebellion in the east.
Separatists in eastern Ukraine have declared their independence from the Kyiv government and support for joining Russia. Violent skirmishes have broken out in numerous eastern Ukraine cities between Ukrainian security forces and the insurgent rebels.
The United States and its European allies have warned Moscow that they will impose new sanctions against key economic sectors of the Russian economy if it disrupts an presidential election to be held on Sunday.
The Ukraine Central Election Commission on Saturday said the unrest could prevent almost two million people from voting.
The commission said it has been unable to prepare for the election in large parts of eastern Ukraine because of threats and "illegal actions" by separatists. Militant pro-Russian groups have taken control of more than a dozen towns and cities since early April.
Some information for this report was provided by AP and AFP.