Igor Girkin, a pro-Russian former paramilitary commander who uses the nom de guerre Igor Strelkov on Telegram, said Russia’s forces had had time to prepare for a Ukrainian counterattack — unlike last year, he wrote, when they created “ideal conditions” for Kyiv’s forces to advance in Kharkiv.

But he said that a significant breakthrough by Ukrainian forces in the Novodonetske area would give Kyiv an opening to drive a wedge between Donetsk and Mariupol in southern Ukraine and cut off communications between the two Russian-held cities.

“If the enemy manages to break through deep enough and on a wide sector of the front (which it is trying to do),” Mr. Girkin wrote, “then its advantage in number of units and formations will be difficult to stop.”

Even as battlefield activities surged, diplomatic efforts to stop the war continued. Pope Francis sent a cardinal to Ukraine on a two-day trip to discuss prospects for peace, the Vatican said on Monday.

There was no immediate comment from the Ukrainian government, which has expressed skepticism about the pope’s role as a potential mediator.

Reporting was contributed by Adam Entous, Paul Sonne, Daniel Victor, Matthew Mpoke Bigg and Gaia Pianigiani.