KYIV, Ukraine—Russia’s decision to change its Ukraine war plan underscores how Moscow is trying to secure territory closest to its own border that it has coveted for years and sets the stage for brutal fighting in an area already devastated by more than a month of war.

With the Russian assault now stretching into a second month, Moscow doesn’t have full control over Ukraine’s Donbas region on the border with Russia. Russian Defense Ministry spokesman Maj. Gen. Igor Konashenkov said Saturday that the country’s forces were fighting to take two villages around Donetsk, a major city held by Russian-backed separatists since 2014.

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