The Russian president's comments came as the military said that some troops were withdrawing from the border near Ukraine - the first sign from Moscow of a possible de-escalation of tensions.
However Western leaders say there is no evidence of the withdrawal yet.
Russia's sudden military build-up prompted fears it would invade Ukraine.
Mr Putin has always denied he is planning an incursion, but tensions have been rising since November, when Russian troops started massing near the border with Ukraine.