MOSCOW — Russian President Vladimir Putin today ordered troops deployed near Ukraine to return to their home bases and praised the launch of a dialogue between the Ukrainian government and its opponents even as fighting continued in the eastern parts of the country.

Putin ordered Defense Minister Sergei Shoigu to pull back forces involved in “planned spring drills” in the Rostov, Belgorod and Bryansk regions to their home bases, the Kremlin said. The order appears to go further than a similar statement by the Russian leader two weeks ago that troops were being pulled back from the border to shooting ranges.

The three regions border Ukraine and the withdrawal of troops deployed there to other Russian provinces would signal a genuine attempt by Moscow to de-escalate the worst crisis in its relations with the West since the Cold War. It also would be easily verifiable by Western intelligence.

The Kremlin statement didn’t say how many troops would be pulled out from the three regions or specify how quick the withdrawal would be.

The United States and NATO said they saw no sign of a pullout after Putin’s earlier claim of a withdrawal.

On Monday, NATO Secretary General Anders Fogh Rasmussen reiterated the military alliance has “not seen any evidence at all that the Russians have started withdrawal of troops from the Ukrainian border.”