The U.S. and its NATO allies flexed their muscles along Russia’s western border this week with military exercises and a pledge of new troops that have deepened Moscow’s fears of U.S. intentions in the region.

Thousands of U.S. and European service members and 50 ships are staging mock assaults on the Baltic coast near Russia as part of the largest U.S.-led exercises there since Russia invaded Crimea five years ago. President Trump on Wednesday committed 1,000 extra troops to Poland, which has become an important military hub....