* Russia says troops pulling back after exercises
* Ukraine, West have voiced alarm over troop build-up (Adds quote and background)
MOSCOW, March 31 (Reuters) - Russia is withdrawing a motorised infantry battalion from a region near Ukraine's eastern border, the Russian Defence Ministry was quoted as saying by state news agencies on Monday.
The United States says progress on resolving the East-West stand-off over Ukraine depends on Russia pulling back troops massed on the border. It was not clear whether other troops would pull back or had already withdrawn.
The Defence Ministry said it was pulling forces out of the Rostov region near Russia's border with Ukraine after month-long military exercises.
"The battalion ... has completed its field exercises at the Kadamovsky training grounds in the Rostov region and is beginning its march to its permanent base in the Samara region," the ministry was quoted as saying.
A battalion numbers between 300 and 1,200 troops.
Russia says the build-up near the border is part of military exercises and there are no plans to move forces across the border into Ukraine, but the United States and NATO have voiced alarm over Moscow's intentions following its annexation of Crimea. (Reporting by Alissa de Carbonnel)