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

Ukrainian troops have reportedly seized a small village on the Russian-occupied eastern bank of Dneipr after crossing the river from the liberated city of Kherson, according to Russian accounts on Tuesday.

A small Ukrainian force has managed to dig in to the village of Dachi after making a landing there a few days ago and are trying to expand the beachhead. Ukrainian troops in small boats crossed the river and landed at the base of the ruined Antonivskiy Bridge, which they destroyed last year.

Russian military bloggers reported very heavy fighting on Tuesday, saying Russian airborne units have been trying unsuccessfully to dislodge the Ukrainians for the past four days. Russian aviation and heavy artillery have been firing on the Ukrainian position.

So far, the Russian side claims some 70 Ukrainian soldiers are dug in, covered by intense artillery fire from across the river. The Russian accounts say Ukraine is trying to move reinforcements across. Video released by Ukraine also shows a Russian APC being destroyed in the village of Oleshkjy, further south, indicating the bank south of Kherson is now contested.

Ukrainian troops have also managed to advance and liberate Rivnopil, a village on the Zaporozhzhia front, breaking through after more than two weeks of fighting. It's notable because the Russians had been fighting hard to hold it.

Taken together the advance there, the landing in Kherson and advances near Bakhmut are small signs the Ukrainian counteroffensive may be starting to pick up steam and the Russians are coming under growing pressure.

-ABC News' Patrick Reevell