REUTERS/Alexei Druzhinin/RIA Novosti/Kremlin
"We were told constantly about concerns over our troops near the Ukrainian border," Putin said after meeting with the Didier Burkhalter, the president of Switzerland and current head of the Organization for Security and Cooperation in Europe, according to the Times.
"We have pulled them back. Today they are not at the Ukrainian border but in places of regular exercises, at training grounds."
Obama administration officials didn't immediately respond to requests for comment on Putin's claims and statements. But according to Reuters, NATO said it has "no indication" of any withdrawal.
"We have no indication of a change in the position of military forces along the Ukraine border," a NATO official told Reuters.
Over the past month, Russia has amassed tens of thousands of troops on the Ukrainian border, stoking fears he could use Russian military forces to intervene in southeastern regions of Ukraine much like they did in Crimea before its annexation. Some observers even worried Russia would invade Ukraine under the pretext of protecting Russian-speaking citizens in the region.
There are plenty of reasons, too, why the areas in which pro-Russian separatists are rebelling are advantageous for Putin, and why he wants to keep those regions under his influence.
Separatists in the region of Donetsk have called for a May 11 referendum to determine whether the region, which comprises the industrial heartland of Ukraine, should become a sovereign state.
Putin's apparent pullback - if not yet clear in troop presence, at least in rhetoric - comes as the West has threatened punishing sanctions if it continues to escalate the situation in Ukraine. Last week, U.S. President Barack Obama and German Chancellor Angela Merkel said they would levy sectoral sanctions on Russia if it disrupted the Ukrainian elections scheduled for May 25.
Assistant Secretary for European and Eurasian Affairs Victoria Nuland went a bit further on Tuesday, telling the Senate Foreign Relations Committee that if Russia supported the May 11 referendum, it could be a "trigger" for more sanctions.