Russian forces launched missile strikes on at least five Ukrainian cities late Wednesday and early Thursday, just hours before Ukrainian President Volodymyr Zelenskyy's planned meeting with U.S. President Joe Biden in Washington, D.C.

Ukrainian Foreign Minister Dmytro Kuleba, who is traveling with Zelenskyy in the United States, described the strikes as "a massive missile attack" on civilian infrastructure, while Ukrainian state-owned grid operator Ukrenergo said it's the first major attack on the country's energy infrastructure in six months.

Russian forces fired a total of 43 missiles across Ukraine from east to west, and 36 of them were shot down by Ukrainian air defense, according to Gen. Valeriy Zaluzhny, commander-in-chief of the Ukrainian Armed Forces. The Ukrainian capital of Kyiv was among the major cities hit, along with areas of Kharkiv, Kherson, Cherkasy, Rivne and Lviv.

Ukrainian authorities were still assessing the damage and casualties on Thursday morning, but dozens of injuries have been reported so far. At least seven people were injured by falling debris in Kyiv.

Meanwhile, rescue efforts were ongoing in the central city of Cherkasy to evacuate as many as 20 people believed to be trapped beneath the rubble of a hotel that was destroyed in the strikes overnight. Thirteen others were already rescued and at least nine were injured, according to Ukrainian officials

The overnight strikes also targeted energy infrastructure in the Rivne region and an industrial zone in the Lviv area.

-ABC News' Victoria Beaulé, Guy Davies, Yulia Drozd and Tatyana Rymarenko.

Russian forces initiated six strikes on Kharkiv overnight, damaging civilian infrastructure, Ukrainian officials said early Thursday.

The mayor of Kyiv also said explosions occurred in the Ukrainian capital overnight. Debris from the downed rockets fell in the Darnytskyi and Holosiivskyi districts of the city.

Five people were hurt in the Darnytskyi district of Kyiv, where the strike also destroyed non-residential buildings. Three of them, including a 9-year-old girl, were hospitalized. Two were treated by medics on scene.

In the Shevchenkivskyi district of Kyiv, rocket debris damaged a gas pipe, an official said.

-ABC News' Will Gretsky

Seventeen people were killed, and 32 others injured, when a Russian missile hit a market in the center of Kostyantynivka in the Donetsk region, according to Ukrainian officials.

"At this moment, the artillery of Russian terrorists has killed 16 people in the city of Kostiantynivka, Donetsk region," President Volodymyr Zelenskyy said on Telegram. "A regular market. Shops. A pharmacy. People who did nothing wrong. Many wounded. Unfortunately, the number of casualties and the injured may rise."

Ukrainian President Volodymyr Zelenskyy visited troops at the front line near Bakhmut as Ukrainian forces continue to make ground in their counteroffensive, the president's office said Tuesday.

Zelenskyy, who was accompanied by commander of ground forces Col. Gen. Oleksandr Syrskyi, thanked soldiers for their service and presented them with awards, according to a video released by the office.

"I awarded the best warriors. And I thank everyone who fights for the sake of the state," Zelenskyy said.

Ukrainian defense forces continue to advance in the direction of Melitopol, according to the spokesman for Pavlo Kovalchuk, the general staff of the Armed Forces of Ukraine.

"They were successful in the direction of Robotyne - Novoprokopivka. They are entrenching at the achieved milestones," the spokesman said.

-ABC News' Will Gretsky

In the wake of Saturday's short-lived attempted rebellion against the Kremlin by the Wagner private military company, Mikhail Khodorkovsky, an exiled oligarch considered one of Putin’s best-known opponents, told ABC News he supports the mutiny and encourages Russians to back the leader of the mercenary group.

Once Russia’s richest man, Khodorkovsky, a Putin opposition activist, spent 10 years imprisoned after he challenged Putin, his case now considered a foundational moment for Putin’s regime.

When Wagner founder Yevgeny Prigozhin and his fighters marched on Moscow Saturday before making a sudden about-face, Khodorkovsky was notable among Russia’s pro-democracy opposition in calling on people to support Prigozhin, arguing that allowing him to remove Putin would create an opportunity for the democrats.

Khodorkovsky told ABC News he believed Prigozhin’s actions were a real coup attempt and that it had “seriously undermined” Putin’s power. He predicted that similar opportunities to collapse the regime will be launched soon.

"The blow to Putin’s reputation, to the authorities’ reputation, was absolutely fantastical," Khodorkovsky said. "Putin’s government today is, without a doubt, strongly undermined by what happened -- his authority, his ability to control the security services is seriously undermined."

Khodorkovsky said Prigozhin’s march on Moscow had undermined Putin’s popularity, showing neither ordinary Russians nor the security services were prepared to act to protect him.

“Along the entire route of Wagner's columns, no one in any way tried to hinder him (Prigozhin). Even the security forces did not try to stop him," Khodorkovsky said. “It showed that, in fact, inside the country, Putin has an absolute void."

Khodorkovsky said he did not support Prigozhin himself -- considering him a "war criminal" -- but that the democratic opposition should have sought to help him overthrow Putin, and then taken power from him after.

Khodorkovsky criticized other parts of the anti-Kremlin opposition who attacked him for calling on people to assist Prigozhin, saying he believed the opposition had “slept through” the opportunity and suggesting it should have sought to stage a rebellion in Moscow at the same time.

"There will definitely now be more such opportunities because of Putin’s weakening. But the next time we need to simply be more ready," said Khodorkovsky, who is living in exile in England. "If an uprising had started in Moscow to meet Prigozhin then a situation could have developed quite differently.

ABC News' Patrick Reevell