KYIV, Ukraine — Russian President Vladimir Putin claimed victory Thursday in the battle for Mariupol despite an estimated 2,000 Ukrainian fighters still holed up at a giant steel mill, ordering his troops not to storm the stronghold but to seal it off “so that not even a fly comes through.”

Putin expressed concern for the lives of Russian troops in deciding against sending them in to clear out the sprawling Azovstal steel mill, where the die-hard defenders were hiding in a maze of underground passageways.

Putin’s comments came as satellite images showed more than 200 new graves in a town where Ukrainian officials say the Russians have been burying Mariupol residents killed in the fighting. The imagery, from Maxar Technologies, shows long rows of graves stretching away from an existing cemetery in the town of Manhush, outside Mariupol.

Mariupol Mayor Vadym Boychenko accused the Russians of “hiding their military crimes” by taking the bodies of civilians from the city and burying them in Manhush.

A man rides his bicycle next to a destroyed Russian tank in Chernihiv, Ukraine, on Thursday. Emilio Morenatti/Associated Press

After nearly two lethal months of bombardment that have largely reduced Mariupol to a smoking ruin, Russian forces appear to control the rest of the strategic southern city, including its vital but now badly damaged port.

But a few thousand Ukrainian troops, by Moscow’s estimate, have stubbornly held out for weeks at the steel plant, despite a pummeling from Russian forces and repeated demands for their surrender. About 1,000 civilians were also trapped there, according to Ukrainian officials.

Instead of sending troops in to finish off the defenders in a potentially bloody frontal assault, Russia apparently intends to maintain the siege and wait for the fighters to surrender when they run out of food or ammunition.

Boychenko rejected any notion that Mariupol had fallen into Russian hands.

“The city was, is and remains Ukrainian,” he declared. “Today our brave warriors, our heroes, are defending our city.”

The capture of Mariupol would represent the Kremlin’s biggest victory yet of the war in Ukraine. It would help Moscow secure more of the coastline, complete a land bridge between Russia and the Crimean Peninsula, which Russia seized in 2014, and free up more forces to join the larger and potentially more consequential battle now underway for Ukraine’s eastern industrial heartland, the Donbas.

A Ukrainian soldier holds a fragment of a Russian multiple missile after recent fights at the village of Berezivka, Ukraine, on Thursday. Efrem Lukatsky/Associated Press

At a joint appearance with Russian Defense Minister Sergei Shoigu, Putin declared, “The completion of combat work to liberate Mariupol is a success,” and he offered congratulations to Shoigu.

Shoigu predicted the steel plant could be taken in three to four days, but Putin said that would be “pointless” and would risk Russian lives.

“There is no need to climb into these catacombs and crawl underground through these industrial facilities,” the Russian leader said. “Block off this industrial area so that not even a fly comes through.”

The plant covers 4 square miles and is threaded with some 15 miles of tunnels and bunkers.

“The Russian agenda now is not to capture these really difficult places where the Ukrainians can hold out in the urban centers, but to try and capture territory and also to encircle the Ukrainian forces and declare a huge victory,” retired British Rear Adm. Chris Parry said.

For weeks now, Russian officials have said capturing the mostly Russian-speaking Donbas is the war’s main objective. Moscow’s forces opened the new phase of the fighting this week along a 300-mile front from the northeastern city of Kharkiv to the Azov Sea.

While Russia continued heavy air and artillery attacks in those areas, it did not appear to gain any significant ground over the past few days, according to military analysts, who said Moscow’s forces were still ramping up the offensive.

A senior U.S. defense official, speaking on condition of anonymity to discuss the Pentagon’s assessment, said the Ukrainians were hindering the Russian effort to push south from Izyum.

Residents walk past a tank destroyed during heavy fighting in an area controlled by Russian-backed separatist forces in Mariupol on Tuesday. Alexei Alexandrov/Associated Press

Rockets struck a neighborhood of Kharkiv on Thursday, and at least two civilians were burned to death in their car. A school and a residential building were also hit, and firefighters tried to put out a blaze and search for anyone trapped.

Western nations, meanwhile, rushed to pour heavy weapons into Ukraine to help it counter the offensive in the east.

U.S. President Biden announced an additional $800 million in military assistance, including heavy artillery, 144,000 rounds of ammunition and drones. But he also warned that the $13.6 billion approved last month by Congress for military and humanitarian aid is “almost exhausted” and more will be needed.

All told, more than 100,000 people were believed trapped with little or no food, water, heat or medicine in Mariupol, which had a prewar population of about 430,000. Over 20,000 people have been killed in the siege, according to Ukrainian authorities.

The city has seized worldwide attention as the scene of some of the worst suffering of the war, including deadly airstrikes on a maternity hospital and a theater.

Ukraine has repeatedly accused Russia of launching attacks to block civilian evacuations from the city. On Thursday, at least two Russian attacks hit the city of Zaporizhzhia, a way station for people fleeing Mariupol, though no one was wounded, the regional governor said.

Britain’s Defense Ministry said that Russia probably wants to demonstrate significant successes ahead of Victory Day on May 9, the proudest day on the Russian calendar, marking the defeat of Nazi Germany in World War II.

“This could affect how quickly and forcefully they attempt to conduct operations in the run-up to this date,” the ministry said.

In the continuing war of sanctions and countersanctions between Russia and the West, Moscow announced it has barred U.S. Vice President Kamala Harris, tech billionaire Mark Zuckerberg and 27 other prominent Americans, including foreign affairs commentators, from entering Russia.

The move was a response to “ever-widening anti-Russian sanctions” by the Biden administration, the ministry said in a statement, and targeted people it said were shaping a “Russophobic narrative.”

Similar restrictions were imposed on 61 Canadians.

Associated Press journalists Mstyslav Chernov and Felipe Dana in Kharkiv, Ukraine; Yesica Fisch in Kramatorsk, Ukraine; Danica Kirka in London; and Robert Burns and Aamer Madhani in Washington contributed to this report, as did other AP staff members around the world.