Dozens of injuries were reported in Kyiv and other Ukrainian cities.
Russia has continued a nearly 19-month-long invasion of neighboring Ukraine. Recently, though, the Ukrainians have gone on a counteroffensive, fighting to reclaim occupied territory.
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A NATO representative said the alliance was watching what was happening in Russia on Saturday.
"We are monitoring the situation," spokesperson Oana Lungescu said.
-ABC News' Rashid Haddou
A governor of the Voronezh region, about 300 miles south of Moscow, says Russia's armed forces are conducting "operational combat operations" there as part of "counter terrorism operation."
Earlier the region's government reported a column of Wagner Group fighters was moving through the region, an area between Rostov-on-Don and Moscow.
"In the bounds of the counterterrorist operation on the territory of the Voronezh region, the armed forces of the Russian Federation are conducting necessary operational combat operations," the official said. "We will inform further about the development of the situation."
-ABC News' Patrick Reevell
Ukrainian President Volodymyr Zelenskyy said Russia appeared to be suffering "full-scale weakness" after the Wagner Group mercenaries said they'd taken hold of a key Russian city.
"Russia used propaganda to mask its weakness and the stupidity of its government. And now there is so much chaos that no lie can hide it," he said on Twitter.
The Wagner Group's Yevgeny Prigozhin responded to Russian President Vladimir Putin's calling him a "traitor," by saying he will not surrender or turn back.
"Putin was deeply mistaken about the betrayal. We are patriots of our homeland, we fought and are fighting," Prighozin said in an audio message. "No one is going to turn around at the request of the president, the FSB or anyone else, because we do not want the country to live longer in corruption, deception and bureaucracy."
Prigozhin accused Russia's military of targeting a Wagner column with helicopters and jets.
-ABC News' Patrick Reevell
