* Russia says troops, equipment leaving three border provinces
* Putin ordered pullback on Monday, saying exercises over
* Pentagon sees small-scale movement, but large force remains (Adds Pentagon comments)
By Thomas Grove
MOSCOW, May 23 (Reuters) - Russia will pull back all forces deployed to regions near its border with Ukraine "within a few days," a deputy defence minister said on Friday, a move that if carried out could ease tensions around Ukraine's presidential election on Sunday.
Moscow has concentrated tens of thousands of troops across the border from eastern Ukraine, where pro-Russian separatists have declared two independent states. The United States said a "very large and very capable" Russian force remained on Friday.
Kiev and its Western allies see the Russian troops as a potential invasion force should Moscow choose to back the rebels openly, fuelling pre-election tensions. The United States and European Union hope the vote will strengthen the embattled central government.
Asked whether Russia would comply with Western calls for a withdrawal of its troops near the Ukraine frontier, Deputy Defence Minister Anatoly Antonov told Reuters: "They will see it - 100 percent ... We will leave less than nothing behind."
The United States said it was not yet convinced.
The Pentagon said it had seen Russian military units withdrawing from the border on a small scale, but it was too early to tell whether that movement represented the broader withdrawal ordered by the Russian President Vladimir Putin.
"We have actually seen the movement of some units away from the border region, apparently back to what we would consider garrison, their home base. But it's not in great number right now," said Rear Admiral John Kirby, a Pentagon spokesman.
He could not say how long it should take the Russian troops to withdraw, but added: "I can tell you they got there in a hurry so it's certainly our expectation that this order to withdraw will be followed with some sense of alacrity. That's what we would like to see."
U.S. State Department spokeswoman Marie Harf said it was "too early to know where or how many of these forces are actually moving out for good."
"And regardless ... the force that remains on the border is very large and very capable and remains in a very coercive position and posture," Harf said.
The Kremlin said on Monday that President Putin had ordered his defence chief to return troops that had taken part in military exercises in the Rostov, Belgorod and Bryansk provinces, which share a border with Ukraine, to their permanent bases.
On Friday, Antonov said Russia had so far moved 20 transport planes and 20 trains carrying personnel and military equipment out of the three provinces, and that a full withdrawal of the forces could be completed "within a few days."
A Defence Ministry source later echoed that statement, saying troops and equipment would be fully moved out of the border area in the course of a few days, but added it would take about 20 days to return the forces to their permanent bases.
Russia has not said how many troops it is withdrawing from areas near the Ukrainian border. The United States and NATO have said Russia amassed some 40,000 troops near the frontier. (Additonal reporting by Eric Beech in Washington; Writing by Alissa de Carbonnel; Editing by Ralph Boulton, Steve Gutterman and Lisa Shumaker)