Washington: A White House spokesman said Wednesday that US officials have seen "no evidence" that Russian troops have pulled back from the tense border with Ukraine.

Russian President Vladimir Putin had earlier said that the estimated 40,000 Russian troops deployed on the frontier had withdrawn to their usual training grounds.

But, speaking to reporters on Air Force One, White House deputy spokesman Josh Earnest said that "to date" there has been "no evidence that such a withdrawal has taken place."

His statements echoed those of NATO, which earlier Wednesday reported "no indication of a change in the position of military forces along the Ukraine border."

Earnest added that Washington would "certainly welcome a meaningful and transparent withdrawal."

"That`s something that we have sought for quite some time," he said.

Earnest made his remarks after the Russian leader met with Swiss President Didier Burkhalter, current chief of the Organization for Security and Cooperation in Europe.

Putin said of the troops he had ordered to Ukraine`s border two months ago: "We have pulled them back. Today they are not at the Ukrainian border but in places of regular exercises, at training grounds."

Putin said he also told pro-Russian separatists "to postpone the referendums planned for May 11 in order to create the conditions necessary for dialogue."

On this point, Earnest repeated the US position that the scheduled votes in southeastern Ukraine -- on declaring greater autonomy or outright independence from Kiev -- were "illegitimate, illegal."

Rather than deferring them, Washington urged that they be cancelled altogether.

"What we`d also like to see is greater support (from Russia) for the ongoing effort by the Ukrainian government to hold free and fair elections on May 25," Earnest said.