A Russian missile attack on a small town in southeastern Ukraine and the fiery inferno that followed killed at least seven civilians, including three children, the country’s authorities said as they surveyed on Sunday the deadly toll of two days of fierce Russian assaults.

Yuriy Borzenko, chief doctor of Zaporizhzhia Regional Children’s Hospital, said in a phone interview that, aside from those killed, dozens of others, including a pregnant woman and five 14-year-old girls, were being treated for wounds after the attack on the southeastern town, Vilniansk, which took place on Saturday.

The girls were out for a walk together in the afternoon sunshine, Dr. Borzenko said, when explosions from the projectiles tore through the center of the town, engulfing shops, cars and homes in flames. Shrapnel had embedded in the skull of one of the girls, who was left in a coma, he said, “still in between life and death.”

“Her parents are in really bad shape, I just saw them,” he added.

As the attacks have rained down, President Volodymyr Zelensky of Ukraine has reiterated his plea to loosen restrictions on the use of long-range American missiles known as ATACMS so that Ukraine can target warplanes at Russian air bases before they take to the sky on bombing runs.

“Long-range strikes and modern air defense are the foundation for stopping the daily Russian terror,” he said on Sunday in a statement accompanying videos said to show the aftermath of a number of the week’s worst attacks.

The strike in Vilniansk was one of a series of attacks across Ukraine, which have killed at least 24 civilians since Friday evening, according to local officials and emergency workers, who said that scores more had been wounded.

Also on Saturday, nine people living in frontline villages in the Donetsk region of eastern Ukraine were killed in Russian shelling, local officials said. At least six more were killed in shelling on Sunday morning, the officials added.

Three powerful guided bombs dropped from Russian warplanes exploded on Saturday in the town of Derhachi, in the Kharkiv region in the northeast, hitting five multistory apartment buildings, Ukrainian officials said. No deaths were reported but two older men were said to have been hospitalized with shrapnel wounds.

Mr. Zelensky said on Sunday that about 800 of those powerful bombs, which are packed with hundreds of pounds of explosives, were dropped by Russian warplanes in the past week.

Although the Ukrainian Air Force said that it shot down 10 Russian drones on Saturday, a 67-year-old man in the southern Kherson region was killed in one such attack, local officials said.

A Russian missile also slammed into a high-rise apartment building in Dnipro, in central Ukraine, on Friday evening. After days combing through the rubble, rescue workers said on Sunday that one person was confirmed killed and two more remained missing.

All of the attacks — reported by local officials reached by phone, the National Police, emergency services and local hospitals, with the aftermath of many captured on video by Ukrainian news outlets — took place within 48 hours and formed only a partial snapshot of the daily violence.

As Russian forces have stepped up assaults at the front, they have also continued to carry out attacks across Ukraine, exploiting gaps in air defenses, with the aim of sapping the country of resources, shattering the economy and breaking public spirit.

The total number of civilians killed in June is not yet available but May was the deadliest month for civilians in Ukraine in a year, according to the United Nations Human Rights Monitoring Mission.

Investigators with the mission reported that at least 174 civilians were killed and 690 others injured in conflict-related violence that month.

The rising death toll has coincided with the continuing bombardment of Ukraine’s power grid, which is making life challenging for millions of residents who have already been enduring hours of scheduled blackouts every day.

Russia has regularly attacked thermal power plants across Ukraine, resulting in the loss of 90 percent of their generating capacity, Ildar Salieiev, the head of DTEK, one of the country’s major private electricity companies, said in a statement.

“Because of the scale of the destruction, repairs will take years rather than months,” Mr. Salieiev wrote.

Ukrainian officials have been trying to prepare the public for what is looking likely to be another difficult winter, and they have been appealing to international allies to speed up the delivery of air defense systems that could limit further damage and save lives.

Even in the best-case scenario — with no further major damage to the grid — energy officials have said that Ukrainians should prepare for a winter of widespread blackouts.

Serhii Kovalenko, the head of Yasno, another private energy company in Ukraine, said that it looked as though there would be a significant daily deficit in the energy system as winter approached.

“If critical infrastructure is repaired and then remaining supplies are distributed, consumers could face a 50 percent deficit,” he said in a statement. “Therefore, the basic forecast is 12 hours without electricity.”

Anna Lukinova contributed reporting from Kyiv. Nataliia Novosolova contributed research.