While Russia launched massive missile strikes across Ukraine overnight, Ukrainian forces have claimed to have attacked a Russian military base on the occupied Crimean Peninsula.

A source in Ukraine's security services told ABC News on Thursday that Ukrainian forces had hit the Saki airfield in Moscow-annexed Crimea, using an initial wave of drones to "overload" Russian air defense. Russian air force assets were then struck using Neptune missiles designed and produced by Ukraine, according to the source.

Multiple unverified videos of the Ukrainian attack were circulating online Thursday.

-ABC News' Yulia Drozd, Oleksiy Pshemyskiy, Tatyana Rymarenko and Tom Soufi-Burridge

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 and U.S. President Joe Biden are set to meet in Lithuania’s capital on Wednesday afternoon, a day after NATO leaders announced during a summit that Ukraine will be allowed to join the alliance "when allies agree and conditions are met" but didn't offer a timeline.

Earlier Wednesday, Zelenskyy held a joint press conference with NATO Secretary-General Jens Stoltenberg, fielding many questions from reporters about Ukraine's path to NATO membership. The Ukrainian president took a noticeably softer tone compared to his remarks the previous day criticizing the lack of a timeline as "unprecedented and absurd."

Zelenskyy told reporters it's difficult as NATO partners are living under different conditions, whereas in Ukraine "survival" matters. He said he understands some people are "afraid" to talk about Ukraine joining NATO because "nobody is willing to have a world war." He acknowledged that his country cannot be a member of the alliance while a war is going on within its borders, but he said "signals are important."

When asked about his upcoming meeting with Biden and how he plans to convince the U.S. president that Ukraine is ready for NATO membership, Zelenskyy responded with gratitude to the United States and confidence that Ukraine will join the alliance once Russia's war is over.

"I'm grateful to President Biden and to the Congress and to the people of United States that are truly the leaders in support and assistance to Ukraine. We highly appreciate this," the Ukrainian president told reporters. "Not planning to find any arguments for making sure that President Biden would see us in NATO. I believe that those arguments, they should be mutual because it's all about this security, the East, the European continent, the Eastern Flank of NATO. And I believe that NATO needs us just as we need NATO. And I believe that this is absolutely fair. I am confident that after the war, Ukraine will be in NATO. We will be doing everything possible to make it happen so that we with the United States would have a same understanding and same vision."

-ABC News' Molly Nagle and Joe Simonetti