The weeks of heavy fighting in Mariupol tied up a significant chunk of Russia’s combat power; at one point the battle was estimated by military analysts to include roughly 10 percent of all the Russian forces in Ukraine.

On Thursday, a Russian video news report from the scene showed a convoy of armored vehicles moving out of Mariupol. Seymon Pegov, a pro-Kremlin reporter embedded with the Russian forces in the city, interviewed Timur Kurilkin, a commander of a separatist battalion from Donetsk, a city in separatist-held eastern Ukraine.

“We are going home, to Donetsk,” said Mr. Kurilkin, walking past the vehicles. “Our next battle is tomorrow,” he said, without specifying where.

In Mariupol, Russia is already seeking to establish authority over civilian life. Denis Pushilin, the head of the self-proclaimed Donetsk People’s Republic, promised high school seniors that they would receive diplomas certified by the separatist entity.

On Wednesday, Andrei Turchak, a top official in Mr. Putin’s party, visited a school in Mariupol, which has already switched to Russian-language curriculum. In a video of his visit, posted to social media, he said, “Many textbooks have already been delivered and these deliveries will continue.”

Anton Troianovski reported from Hamburg, Germany, Ivan Nechepurenko from Tbilisi, Georgia, and Richard Pérez-Peña from New York. Reporting was contributed by Michael Schwirtz from Zaporizhzhia, Ukraine, David E. Sanger and Zach Montague from Washington, Neil MacFarquhar from Istanbul, Matthew Mpoke Bigg from London, Alan Yuhas from New York, and Cora Engelbrecht from Krakow, Poland.