MOSCOW, May 19 - The Kremlin announced on Monday President Vladimir Putin had ordered Russian forces near Ukraine back to their bases, but NATO and the United States said they saw no sign of a pullback and Moscow had failed to carry out such promises before, Reuters reported.

Moscow has massed tens of thousands of troops near the border regions where pro-Russian separatists have declared independent states, and Kiev and its Western allies fear they could be used to invade in support of the rebels.

Ukraine holds a presidential election on Sunday which Western countries consider a crucial event in resolving the country's crisis. The United States and EU have threatened to ramp up sanctions on Moscow if it interferes in the vote.

Ukrainian border guards said there had indeed been a decrease in Russian military activity close to the border. But the United States and the Western military alliance said there was no indication troops had pulled back.

"Unfortunately, I have to say that we haven't seen any evidence at all that the Russians have started a withdrawal of troops from the Ukraine borders," NATO Secretary-General Anders Fogh Rasmussen told a news conference in Brussels.

White House spokesman Jay Carney said the United States had seen reports Putin had ordered Russian troops back to bases but "at this point we see no indication of any movement".

Pentagon spokesman Rear Admiral John Kirby told Reuters: "We have seen no indication of any movement."

A Reuters cameraman saw over a dozen tanks leaving a training ground in the Rostov region. Russian state television also showed pictures of a similar number of tanks leaving a training facility in the Belgorod region.

Putin declared the right to send forces to Ukraine to protect Russian-speakers if necessary in March and quickly annexed Ukraine's Crimea region, after a pro-Russian president was toppled in street demonstrations in Kiev in February.

Armed rebels, many led by a Muscovite enthusiast of historical battle re-enactments, have seized towns and cities in eastern Russia and held a vote on independence which Western countries describe as a sham.

NATO and the United States say previous Russian pledges to pull back troops - including an announcement by Putin himself on May 7 that they had already been withdrawn - produced no significant withdrawal.

"Now I think it's the third Putin statement on withdrawal of Russian troops but so far we haven't seen any withdrawal at all," Rasmussen said on Monday. "I strongly regret that, because a withdrawal of Russian troops would be a first important contribution to de-escalating the crisis."

Ukraine's border guards did not speak directly about a withdrawal but said they had noticed a decrease in activity by Russian forces across the frontier.

"Before, we would see 10 or more aircraft flying along the border in a 24-hour period, and military vehicles would come directly up to the border. Now there are no such instances," border guards spokesman Oleh Slobodyan said. (rt/ez)