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."

Beginning in October, the U.S. will provide F-16 training to a small number of Ukrainian pilots and maintenance teams, Pentagon press secretary Brig. Gen. Pat Ryder said Thursday.

Ryder said "several" pilots and "dozens" of aircraft maintenance personnel will begin training at Morris Air National Guard Base in Tucson, Arizona, after they receive English training in September at Lackland AFB in San Antonio, Texas. The number of pilots and personnel will be determined by Ukraine.

"Although some Ukrainian pilots have English language skills we are anticipating that all the pilots coming to the United States will require some level of additional English language instruction, given the complexities and the specialized English that's required to fly these aircraft," said Ryder.

Sabrina Singh, the Pentagon's deputy press secretary, told reporters earlier this week that the U.S. was open to the idea of training on F-16's if European countries reached capacity though she couldn't define what numbers would constitute capacity. Ryder on Thursday also wouldn't provide a number and said the U.S. wasn't going to wait for the Netherlands and Denmark to reach capacity.

"We know that as the Danes and the Dutch prepare to train those pilots that at a certain point in time in the future, capacity will be reached. So preemptively acknowledging that and leaning forward in order to to assist with this effort is the impetus for why we're doing this now," said Ryder.

Ryder wouldn't get into when F-16 deliveries to Ukraine might begin. Denmark's Prime Minister said over the weekend that the first Danish F-16's could arrive by New Year's.

-ABC News' Luis Martinez