MOSCOW, Nov 25 (Reuters) - Russia"s military is tracking the guided missile destroyer USS Arleigh Burke after it entered the Black Sea to patrol with NATO allies, TASS news agency cited the Russian defence ministry as saying on Thursday. The manoeuvre comes at a time of high tension in the region, with Russia, Ukraine and NATO all conducting military drills in recent weeks and Moscow denying suspicions by Kyiv and Washington that it is contemplating an invasion of Ukraine. The U.S. Sixth Fleet said the Arleigh Burke had entered the Black Sea on a routine patrol, a day after Russia said it had conducted military drills there involving aircraft and ships. "While in the Black Sea, the ship will operate alongside NATO allies and partners in the region, working together to ensure security and stability in this vital international waterway," it said in a statement. Ukraine has tilted towards the West and away from Moscow"s orbit since 2014, when a pro-Russian president was ousted after mass protests. It is not a NATO member but enjoys backing from Washington, including defence aid and supplies of patrol vessels and anti-tank weapons. The Arleigh Burke"s mission follows a similar visit to the Black Sea earlier this month by the command ship USS Mount Whitney, which was also tracked closely by Russia"s navy. read more