Regardless of the excessive price in lives, Ukrainian and Russian leaders mentioned that the battle for Bakhmut would rage on, at the same time as they brace for a struggle that they anticipate to widen and intensify because the climate warms.

Officers in each Kyiv and Moscow predicted that Ukraine, taking supply of Western tanks, missiles and different arms, would quickly launch a renewed push to reclaim territory misplaced within the east and south.

The Ukrainians “are getting ready for numerous offensive operations — everybody is aware of that,” Dmitri A. Medvedev, a former president of Russia and vice chairman of President Vladimir V. Putin’s Safety Council, mentioned in feedback launched on Friday. “Our Common Employees is taking this into consideration and getting ready its options.” The spokesman for President Biden’s Nationwide Safety Council mentioned this week that Russia was planning new assaults, as properly.

However even with that prospect looming, nobody is predicting a letup within the lengthy, brutal struggle for Bakhmut, the jap Ukrainian metropolis that has skilled the bloodiest fight of current months. Oleksandr Syrsky, the commander of Ukraine’s floor forces, mentioned on Thursday that Russian forces had been “not giving up hope of taking Bakhmut at any price,” however he mentioned they gave the impression to be “shedding vital energy and changing into exhausted.”

However he added that the Kremlin wanted to outline its total targets in Ukraine clearly, and regardless of the expectations of escalating offensives, he spoke of tips on how to finish a struggle that has exacted a fearsome toll on each nations.

“To begin with, we have to resolve the place we’re going to or the place we come to a halt,” Mr. Prigozhin mentioned in an interview posted to the Telegram messaging community on Thursday. “As quickly as that is decided completely clearly, then will probably be clear when the S.V.O. will finish,” he mentioned, utilizing the Russian initials for the Kremlin’s time period for the invasion it launched 13 months in the past, which it calls a “particular navy operation.”

He isn’t the primary supporter of Russia’s struggle effort to counsel unclear goals and a weariness with a struggle that has been a lot more durable than anticipated.

Russian forces maintain many of the jap Donbas area that features Bakhmut, and Mr. Putin has urged that, at a minimal, Russia should full the conquest of the 2 provinces that make up the Donbas and maintain on to Crimea, which it seized in 2014. However his authorities has additionally claimed to annex two different provinces the place it holds some territory, and Mr. Putin has at instances hinted at erasing Ukraine as a separate state. He has additionally mentioned, falsely, that Ukraine is managed by Nazis whom Russia should remove.

Mr. Prigozhin — the once-secretive tycoon whose shut private ties to Mr. Putin helped him amass a fortune — has regularly criticized Russian navy officers as inept and jealous, complaining that they withhold assets from Wagner. And his boastful social media presence more and more has parts of pessimism; he urged just lately that Wagner may quickly be a spent pressure and {that a} Ukrainian offensive may lower off its fighters in Bakhmut.

He has additionally edged nearer to disagreeing publicly with Mr. Putin particularly, as within the suggestion that the struggle goals are unclear, although he didn’t cite the Russian chief by title. In his put up on Thursday, he mentioned: “I don’t know in regards to the denazification of Ukraine. Are there Nazis there, or aren’t there? I haven’t crawled round in there.”

Western analysts debate whether or not Russia’s battered navy, after struggling immense casualties and depleting its weapon shops, is able to mounting a much wider marketing campaign than the one it’s sputtering via now.

Mr. Putin has sought assist from China, which has offered surveillance drones however to date not weaponry, Western governments say, and he performed host this week in Moscow to the Chinese language chief Xi Jinping. China has aligned itself with Russia, with out overtly taking sides within the struggle, and so they share a standard antagonist in the USA.

President Volodymyr Zelensky of Ukraine may be very keen to maintain China on the sidelines. He has tried to keep up ties to Beijing and has been cautious to not criticize Mr. Xi publicly, and a senior Ukrainian official mentioned on Friday that Kyiv was making an attempt to rearrange a telephone name between the 2 leaders.

China is a crucial diplomatic ally, buying and selling companion and potential supply of arms to Russia because the Kremlin faces rising worldwide isolation and condemnation.

Final week, the Worldwide Prison Court docket issued an arrest warrant for Mr. Putin for delivery hundreds of Ukrainian youngsters from captured territory to Russia, the place they’re positioned with households or in facilities to indoctrinate them in pro-Russian views. Ukraine and human rights teams have known as the trouble outright abduction and a step towards erasing Ukrainian cultural identification. The European Union mentioned it will set up an effort to trace the lacking youngsters.

In Washington, a bipartisan group of senators despatched a letter to President Biden on Friday, asking him to share with the I.C.C. any proof of struggle crimes gathered by U.S. intelligence businesses. Although the USA has lengthy refused involvement within the courtroom, Congress final 12 months licensed the sharing of intelligence with it particularly for the struggle in Ukraine.

The worldwide courtroom will open a area workplace in Ukraine to research violations of worldwide legislation within the struggle, the courtroom and the Ukrainian authorities mentioned on Thursday.

Authorized specialists say that the Russian invasion itself is likely to be a violation of worldwide legislation, together with the hundreds of aerial strikes on Ukrainian civilian targets, and there have been well-documented mass atrocities by Russian floor forces.

However there’s additionally proof that prison conduct has gone in each instructions. The United Nations mentioned on Friday that it had documented abstract executions of dozens of captured troopers by each Ukrainians and Russians.

On the battle strains, each side have poured large assets into Bakhmut, which Russia has did not seize regardless of eight months of combating. Hundreds — presumably tens of hundreds — of troops have been killed or wounded there, and the Russian losses have been particularly heavy, with Wagner typically utilizing fighters recruited from prisons in near-suicidal assaults.

The casualties have given Bakhmut symbolic that means past the strategic significance of a small metropolis that straddles a couple of highways and railroads. Although Russian forces have closed in on it from three instructions, they’ve been unable to rout the Ukrainian defenders or wrest management of the final roads main west out of town, which Kyiv’s forces use to maneuver folks and provides.

After months of shelling, town’s buildings are nearly all in ruins. There may be street-by-street, building-by-building fight, with the opposing forces holed up within the blasted shells of deserted factories, in response to Russian and Ukrainian accounts of the combating.

And but some civilians stay. From a prewar inhabitants of 70,000, fewer than 3,500 residents are nonetheless in Bakhmut, together with 32 youngsters, in response to Pavlo Kyrylenko, the Ukrainian governor of the encircling Donetsk Province.

The Ukrainian authorities stepped up calls final month for all residents to depart town and ordered the final assist teams there to depart, in what was then seen as a potential prelude to a withdrawal as Russian troops closed in.

“These are those that refuse point-blank to depart town,” Mr. Kyrylenko instructed reporters. “An incredible quantity of labor has been executed to evacuate them.”

Some Bakhmut residents “are even hiding” from cops and emergency staff who go to their properties, he mentioned.

However risks linger, even for individuals who escape town. Early Friday, Russian missiles struck town of Kostiantynivka, about 13 miles southwest of Bakhmut, in response to a press release from Ukraine’s common prosecutor’s workplace. One missile hit an “invincibility middle,” considered one of hundreds of makeshift shelters Ukraine has arrange nationwide to offer fundamental providers throughout Russian assaults.

Three girls who had fled to Kostiantynivka from close by areas, together with one from Bakhmut, died within the strike, the prosecutor’s workplace mentioned.

Reporting was contributed by Charlie Savage, Matthew Mpoke Bigg, Victoria Kim and Monika Pronczuk.