BRUSSELS—The European Union has slammed the brakes on two big Russian pipeline projects to supply more natural gas to Europe, as part of its efforts to turn up the heat on Moscow over its incursion into Crimea.

The move will deal a blow to Russia's ambitions of increasing its gas exports and bypassing Ukraine as a transit country. It comes as the 28-country bloc is weighing other options to reduce its dependence on Russian natural gas, which accounts for over a third of EU supplies. Six EU countries, including Bulgaria and...