RUBTSY, Ukraine—The Ukrainian military offensive that ousted Russian troops from the Kharkiv region early this month has now crossed deep into the northern part of the nearby Donetsk region, increasingly threatening Russian control over lands that Moscow seeks to annex as sovereign territory in coming days. Here in Rubtsy, a village in Donetsk that Russia captured in late April, advancing Ukrainian forces stream east past burned-out carcasses of Russian tanks and the bloated bodies of Russian soldiers that remain on roadsides. Trophy pieces of Russian armor are being towed in the opposite way, to be repaired and reused.

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