“Of course, getting control of such an important center in the south as Mariupol is a success,” Mr. Putin was shown telling Mr. Shoigu, though the city is not yet fully under Russian control. “Congratulations.”

The fight for Mariupol carries enormous significance for both sides. It is the last pocket of serious resistance in the land bridge the Kremlin has created between territory it already holds in the Donbas region in the east and the Crimean Peninsula in the south. It is also home to much of Ukraine’s Azov Battalion, filled with far-right fighters who give a sheen of credibility to Mr. Putin’s false claim that Ukraine is run by Nazis and that he is “denazifying” the country.

The battle for the city also illustrates both the brutality of the Russian invasion and its struggles — truths that have galvanized much of the world but that Moscow has worked hard to conceal from its own people. Mariupol has been under siege for more than a month, much of it lies in ruins, and satellite images show a growing mass grave on the city’s outskirts. Roughly three-quarters of the residents have fled and, according to Ukrainian officials, about 20,000 civilians there have been killed — yet it is still not fully conquered.

Russia is shifting the focus of the war to gaining territory and wiping out Ukrainian forces in Donbas, where Moscow-backed separatists have been fighting Ukraine since 2014. Britain’s Defense Ministry said Thursday in an intelligence assessment that the Kremlin is eager to make swift gains that it can trumpet on May 9, at the annual celebrations of victory over Nazi Germany in 1945.

At the White House, President Biden said the fight for Donbas was “going to be more limited in terms of geography but not in terms of brutality,” compared to the early phase of the war. But, he added, Russia will “never succeed in dominating and occupying all of Ukraine.”

Mr. Biden announced another $800 million package of weapons for Ukraine, including dozens of heavy howitzers, 144,000 shells for them, and tactical drones, bringing total military aid this year to well above $3 billion. The weapons supplied by NATO nations are becoming increasingly heavy and sophisticated, reflecting an expected shift in the nature of combat as the war pivots to Donbas, but the president said some of armaments will remain secret.

“We won’t always be able to advertise everything that we, that our partners are doing,” Mr. Biden said. Referring to the U.S.-made antitank missile that Ukrainians have used to devastating effect, he added, “To modernize Teddy Roosevelt’s advice, sometimes we will speak softly and carry a large Javelin.”

Mr. Biden also banned ships tied to Russia from U.S. ports, and announced $500 million in economic aid to Ukraine — though the government in Kyiv told the International Monetary Fund that over the next three months it will need $15 billion. The White House also detailed plans for accepting up to 100,000 refugees from Ukraine, saying that U.S. citizens can begin applying to sponsor the immigrants on Monday.

The war in Ukraine took center stage in the French presidential campaign in a televised debate Wednesday night between President Emmanuel Macron and his far-right challenger, Marine Le Pen, who has in the past praised Mr. Putin. She spoke against arming Ukraine and said Mr. Macron’s efforts to cut imports of Russian energy would hurt France economically. He replied, “you are, in fact, in Russia’s grip,” noting that Ms. Le Pen’s party had borrowed from a Kremlin-linked bank.

The Kremlin worked quickly to portray the battle for Mariupol as a success. Dmitri S. Peskov, Mr. Putin’s spokesman, told reporters that there was now “an opportunity to start establishing a peaceful life” in Mariupol and start “returning the population to their homes.”

Mr. Peskov described the Azovstal steel plant — an immense Soviet-era complex near the city center — as “a separate facility” with no impact on life elsewhere in the city. Ukrainian fighters have been hiding for weeks in the plant’s underground bunkers, along with about 1,000 civilians, amid rising concerns they lack food and water.

Ramzan Kadyrov, the strongman leader of the southern Russian republic of Chechnya, said on Wednesday that his troops would soon help Russia capture the Azovstal plant in its entirety. In Thursday’s televised meeting, Mr. Shoigu told Mr. Putin that it would take three to four days to clear the plant.

But Mr. Putin responded by calling the storming of the plant “impractical,” and added, “I order it to be canceled.”

It was not clear what that would mean on the ground; shelling and rocket attacks on the steel mill complex continued on Thursday, Staff Sgt. Leonid Kuznetsov of the Ukrainian National Guard, one of the soldiers there, said via text message. He said that shortly before he heard about Mr. Putin’s public order, Russian troops had attempted to storm the plant, coming within about 20 meters of his hide-out. The Ukrainians, he said, were running out of ammunition.

In directing Mr. Shoigu on a national broadcast, Mr. Putin, who made the decision to go to war, presented himself as a rational and humane leader. “This is the case when we must think — that is, we must always think, but even more so in this case — about preserving the life and health of our soldiers and officers,” he said. “There is no need to climb into these catacombs and crawl underground through these industrial facilities.”

Implicit in his statement was a potential credibility challenge for Mr. Putin, stemming from his unwillingness to admit setbacks and blunders in the war to his own people. The government and military have not acknowledged the deaths of Russian sailors on the missile cruiser Moskva, pride of Russia’s Black Sea fleet, which was sunk last week, but information about missing troops is increasingly circulating online.

Coming after Russia’s decision last month to abandon its stalled campaign in the north of Ukraine, the sinking of the Moskva — Ukraine claims to have hit it with two missiles — and the morass in Mariupol, once a thriving industrial and shipping hub, underscore the systemic weaknesses bedeviling the Russian military.

But costly as Mariupol has been for Russia, it is far costlier for Ukraine. Civilian casualties are high, though for now there are only rough estimates, and nearly all the vital infrastructure — including some of Ukraine’s biggest export-oriented enterprises — have been destroyed. Hospitals, theaters, schools and homes have been reduced to rubble.

President Volodymyr Zelensky of Ukraine said on Thursday that he would trade Russian soldiers who had been taken prisoner for the civilians sheltered at Azovstal, but he said that Russia had not yet responded to the offer.

Agreements to evacuate civilians en masse or bring in vital aid have mostly been thwarted, and have sometimes turned deadly, largely because Russian units have halted or fired on aid convoys. But day by day, people have managed to escape, on their own or in small groups.

On Thursday, a yellow bus carrying dozens of people from Mariupol arrived in the central Ukrainian city of Zaporizhzhia, where passengers described weeks hiding in basements, cold and hungry, amid endless shelling. They escaped in a harrowing, all-night drive through Russian-held territory, past countless checkpoints manned by jumpy Russian soldiers.

“In the city everything is destroyed, it’s terrifying,” said Matvei Popko, 10, who had fled with his mother, father and grandmother. “At any moment your home could get hit and collapse. For a little more than a month we lived in the basement.”

Ukrainian officials have accused Russia of forcibly deporting hundreds of thousands of civilians, including a large number from the Mariupol area, to Russian territory, for use as propaganda fodder and a bargaining chip. Russia denies the charge, which is a potential war crime.

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.