KHARKIV, Ukraine—Ukrainian officials accused Russia of burying thousands of civilians in mass graves outside Mariupol, a city now mostly under Russian control after two months of fighting, as Moscow pressed its offensive to capture the rest of the country’s eastern Donbas region.

A senior Russian military official, meanwhile, said Russia’s territorial goals extend well beyond Donbas, which Moscow stopped considering as part of Ukraine when President Vladimir Putin in February recognized the independence of the so-called Donetsk and Luhansk people’s republics, statelets created with Moscow’s help in 2014.

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