BRUSSELS—U.S. fighter planes will conduct patrols with the Bulgarian air force next month, U.S. and Bulgarian officials said Wednesday, operations that are aimed at opening a new front in the NATO alliance’s efforts to deter Russian military aggression.

The North Atlantic Treaty Organization has increased its existing air-policing efforts in the Baltic countries since Russia’s annexation of Crimea, and some members of the Western military alliance have been pushing for more operations around the Black Sea region.

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