Russia canceled a bid to have Syria-bound warships refuel on Spanish territory as tensions rose between Moscow and the North Atlantic Treaty Organization over Russian ships deploying in the Baltic Sea and new NATO measures to reinforce Eastern European allies.

Moscow rescinded its request to Spanish authorities to allow a flotilla to refuel at Spain’s North African exclave of Ceuta, according to Spain’s Foreign Ministry and Russian state media, a switch that came as Madrid faced rising pressure from U.S. and U.K. officials...