The administration of U.S. President Barack Obama has not received any evidence of the withdrawal of Russian military from the border with Ukraine, the press secretary of the White House, Jay Carney, said.

Speaking at a regular briefing on Monday, Carney said Washington sees Russian President Vladimir Putin's order to withdraw the troops as "a welcome announcement," while noting that the U.S. has "heard that promise before, and have yet to see any indication that it's been fulfilled."

As reported, Russian President Vladimir Putin instructed on Monday the Defense Minister, Sergei Shoigu, that troops return to base after taking part in drills in the Rostov, Belgorod and Bryansk regions; the spring phase of military training has been completed, the Kremlin said.

"Due to the completion of the routine spring phase of military training that involved redeployment, in particular, at training sites in the Rostov, Belgorod and Bryansk regions, Putin has ordered the defense minister that the troops, which took part in the exercises, return to their home bases and continue military training in nearby training sites," the president's press office said.