Wagner Group forces launched attacks from several directions on the city of Bakhmut, though analysts said seizing it would yield little strategic value.

After weeks of unexpected battlefield setbacks for Russia, the war in Ukraine on Sunday delivered another surprise: the emergence of a former Russian convict and onetime hot-dog seller as perhaps the Kremlin’s best hope for a small, face-saving military victory.

With occupying Russian forces at peril in the strategic southern city of Kherson, troops with a private military force controlled by Yevgeny V. Prigozhin, a convicted thief and longtime associate of Russia’s president, Vladimir. V. Putin, advanced on the Ukrainian-held city of Bakhmut in the east of the country.