WASHINGTON—The U.S. is close to imposing the toughest round of energy sanctions so far on Russia, measures that would also hit Western companies like Exxon Mobil that are working with Russian state-controlled oil companies.

The sanctions, which the European Union is expected to match, would ban energy companies from working with Russia on future oil exploration in the Russian Arctic, deep seas and shale rock formations, according to a U.S. official.

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