ENI only breaks even on its gas dealings with Gazprom. ENI’s gas unit lost 660 million euros, or $913 million, in 2013.

Even so, one of Mr. Scaroni’s biggest worries now is ENI’s deep engagement with Gazprom. It operates not only as a distributor but also as a partner on a planned new gas pipeline called South Stream that would run from Russia under the Black Sea, avoiding Ukraine to run through countries like Bulgaria and Hungary and ending in northern Italy.

The pipeline would be a major new source of Russian gas for energy-hungry Europe. But European Union authorities have become deeply skeptical about the South Stream plan, seeing it as just another way of making Europe more dependent on Russian energy. They have shown far greater enthusiasm for plans to deliver gas along a so-called Southern Corridor pipeline from Azerbaijan in the Caspian region and could run through countries including Turkey, Albania, Greece and Italy.

Mr. Scaroni worries that the portion of ENI’s gas from Russia that passes through Ukraine might be severed at any moment through contract disputes or if fighting broke out. He also worries that ENI and other energy companies might be ordered by Europe and the United States to stop buying Russian gas as part of tougher sanctions.

Given the balance of interests, tighter sanctions by Western governments might more likely aim to stem the technology that Russia needs to increase its future production, rather than to cut off gas supplies to Europe, said David L. Goldwyn, a special envoy and coordinator for international energy affairs from 2009 to 2011 at the United States Department of State.

“No one seeks an outcome that would hurt Europe as much as Russia,” he said.

Tensions between Europe and Russia over energy have been mounting for years, partly because of previous standoffs between Kiev and Moscow that temporarily blocked supplies to the European Union. Those outages in 2006 and 2009 are a top reason that the European Union had already been trying to chip away at Europe’s dependence on Russia even before the Crimea annexation.

Despite those efforts, there are few signs that the mutual dependence they share will diminish anytime soon.