adept at attacking Russian command and control hubs and destroying large amounts of Russian equipment. On Monday, the Biden administration announced another round of support for Ukraine: $550 million in military aid, including more ammunition for 155-millimeter howitzer artillery pieces and High Mobility Artillery Rocket Systems, or HIMARS, that the United States has already provided.

But for all its sluggish or faltering progress in the war, Russia retains vast advantages in the size of its arsenal, and its military has shown a willingness and ability to strike all over the country, even as it focuses on gaining ground in eastern Ukraine. There, Russia has blanketed town after town with overwhelming artillery fire as it tries to reposition ground forces to press forward.

The strategy slowly gave Russia control of the eastern Luhansk Province, leaving many cities and villages in ruins. Russian forces have since moved to reinforce the south and to push into another eastern province, Donetsk.

“Their tactic remains much the same as it was during the hostilities in Luhansk region,” Serhiy Haidai, head of Ukraine’s Luhansk regional government, said on Monday.

He said the Russians were making daily attempts to mount an offensive on the city of Bakhmut, in Donetsk, but so far had failed to break through the main Ukrainian defensive lines.

Russian forces have also continued to shell residential and military areas in and around the city of Kharkiv in the northeast, putting pressure on Ukraine not to shift too many of its defenses from there.

In Chuhuiv, in the Kharkiv region and just 10 miles from Russian lines, residents were still recovering on Monday from missile strikes last week on the House of Culture, a building used since Soviet times for cultural events. In wartime, the building’s kitchens were used to prepare food for the needy, but members of the city government had also used it as a temporary office, possibly a reason for the attack.

The missiles killed three people sheltering in the basement and wounded several more, according to Oleh Synyehubov, the Kharkiv regional administrator. A volunteer cook was among the dead, residents said. His brother and several other people survived.

Two women were also killed, one of whom had been helping the cook, said a resident who gave only his first name, Maksim, wary of possible retribution. They were making an Uzbek rice dish, plov, for people in the neighborhood.

“She was just cleaning vegetables,” Maksim said.

Chuhuiv has come under increasing bombardment in recent days, as have the city of Kharkiv and other villages and towns in the province. Soldiers guarding the approaches to the city on Sunday said that artillery strikes had been steady much of the day, hitting an industrial area around the train station.

The Russians “are hitting lots of places like this, all the schools as well,” said Maksim. “They are doing it to make the people leave.”

People were getting the message, and the town was largely empty, he said. He was preparing to leave too, he said. He and his family had plans to emigrate to Canada.

“There is nothing left here,” he said.

Michael Schwirtz reported from Mykolaiv, Ukraine, Matina Stevis-Gridneff from Brussels and Matthew Mpoke Bigg from London. Reporting was contributed by Carlotta Gall and Kamila Hrabchuk from Chuhuiv, Ukraine, Marc Santora from London and Alan Yuhas from New York.

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