Russia launched a new swarm of Iranian-made drones overnight, Ukraine’s Air Force said on Saturday, attacking critical infrastructure in several regions after unleashing a barrage of cruise missiles, antiaircraft missiles and drones on cities across Ukraine.

The overnight drone attack caused serious damage to Ukraine’s already battered power grid, which Russia has repeatedly targeted in what military analysts say is a strategy of plunging the country into cold and darkness to lower morale.

The strikes, the first heavy aerial assault in weeks, occurred as fighting on the ground has intensified, with Ukrainian officials saying that Russian forces are mounting a major new push to seize control of the entire Donbas region of eastern Ukraine.

Air-defense systems destroyed 20 of the Shahed 136 drones between 6 p.m. and midnight, the Ukrainian Air Force said in a statement early Saturday. But three energy facilities in the Dnipro region of southeastern Ukraine were hit, including one in Kryvyi Rih for the second time in a day.

“They targeted our critical infrastructure,” Serhii Lysak, the head of the regional military administration, said in a statement on the Telegram messaging app.

Drones were downed over the southern regions of Kherson, Mykolaiv and Odesa, the Kyiv Independent reported, citing the Ukrainian military’s southern command.

The drone attack occurred after Russian forces fired more than 100 missiles in a day of strikes across Ukraine, in what the Ukrainian air force described as a “massive” assault. Officials were still assessing the scope of the destruction, but the state-owned power utility said that several thermal and hydroelectric power plants had been badly hit.

“The scale of the damage is significant,” Volodymyr Kudrytskyi, the company’s chief, told Ukrainian television on Friday.

As the war nears its first anniversary, Russia has been pouring troops and equipment into eastern Ukraine, in the early stage of what Ukrainian and Western officials say is expected to be a major offensive.

Ukraine’s Western allies have been rushing to provide more powerful weapons so that Kyiv can mount its own offensive. The government of President Volodymyr Zelensky has reiterated its calls for even more arms — and faster delivery.

Mr. Zelensky said he had received “good signals” from allies when he pressed his case for heavier weapons on a rare international trip this past week to London, Paris and Brussels.

“This applies both to long-range missiles and tanks, and to the next level of our cooperation — combat aircraft. But we still need to work on this,” he said on Friday in his nightly address.

John F. Kirby, a White House spokesman, on Friday predicted that the coming weeks and months would be “difficult and critical” for Ukraine. He said that while he had yet to see a major new offensive take shape, “we’re anticipating that and, frankly, so are the Ukrainians,”

The United States believes that President Vladimir V. Putin of Russia will “take advantage” of the winter months to “restock, resupply, rearm” for what could be renewed offensive operations in the spring, Mr. Kirby told a press briefing on Friday. “As the weather improves, the fighting will probably get more vicious,” Mr. Kirby said.

In recent weeks, some of the fiercest fighting has centered on the Russian-occupied city of Kreminna and the Ukrainian-held city of Bakhmut, which are about 30 miles apart in the Donbas region.

Ukraine’s military said early Saturday that Bakhmut remained the main focus of Russian forces, with 124 strikes and 54 “clashes” in the area over the past day. Moscow sees the city as a key jumping-off point for attacking the Ukrainian stronghold at Kramatorsk, a crucial step toward taking all of Donbas.