"I can report to you that we have seen some indications of activity on the border but it's too early to conclude that that activity indicates a withdrawal from the border," White House spokesman Jay Carney said.
"Should this be the beginning of a withdrawal, we would welcome such an effort," Carney added, speaking four days before the presidential vote in Ukraine on Sunday.
Putin on Monday announced that the troops, estimated by NATO to number 40,000, were to return to bases after the end of spring exercises.
"We've seen in the past some movements, a battalion comes, a battalion comes in, and you still have a huge and unprecedented presence of Russian troops on the Ukrainian border which can only serve to intimidate and destabilise Ukraine," Carney said.
Confusion has reigned over the status of Russian troops which have massed along the Ukraine border since March.
Ukrainian border guards can no longer see Russian troop movements across the frontier but neither the United States nor NATO has been able to confirm a complete withdrawal as announced on Monday by the Kremlin.
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