A local woman welcomes armed pro-Russia militia men marching towards a polling station during a referendum in the eastern Ukrainian city of Slaviansk on May 11, 2014. Picture: Yannis Behrakis

Washington - The United States on Monday demanded “firm evidence” that Russia was withdrawing its forces from the borders of Ukraine, saying it had so far seen no sign of such a redeployment.

US officials said a withdrawal, ordered by Russian President Vladimir Putin, would be welcome if it occurred, but expressed skepticism that it was underway.

Russia said that it had ordered the end of military exercises near its border with Ukraine, days ahead of a crucial presidential vote aimed at bringing the country out of crisis.

In a move that could ease tensions, Putin's office said he had ordered thousands of Russian troops deployed in border regions to return to barracks after the end of spring exercises.

A senior US official insisted that the troops had never been conducting “exercises” near the border.

“They've been up (on) the border in a menacing posture,” he said, and cautioned that so far “we haven't seen evidence of them” withdrawing.

“We'll want to see clear, firm evidence of this move before we make any judgment,” the official said.

White House spokesman Jay Carney said at this point the administration saw “no evidence of any movement, which has been the case several times before.”

“We would know and would be able to confirm for you if the Russian military had moved back,” Carney told reporters, in an apparent reference to US spying technology.

Earlier, NATO Secretary General Anders Fogh Rasmussen said he had no evidence that Russian troops were withdrawing from border positions.