KYIV, Ukraine—Russia ordered its forces to target the long-range missiles and artillery weapons that Western countries have recently supplied to Ukraine, a sign of how Kyiv’s additional firepower has begun to reshape the conflict. On Monday, Defense Minister Sergei Shoigu told a group of Russian troops to make Ukraine’s long-range weaponry a priority target to prevent shelling in parts of eastern Ukraine held by Russian forces, according to the Russian Defense Ministry. A recent shipment of advanced Western weapons has reinforced Ukraine’s efforts to fend off Russia’s invasion. Whether those weapons will enable Kyiv to turn the tide remains unclear,...