Ukrainian President Volodymyr Zelenskyy said in a Telegram post that he spoke with President Joe Biden who offered greetings on the Independence Day of Ukraine.

Zelenskyy in return thanked Biden for America's support during the war.

"The U.S. took the lead in rallying global support for Ukraine. This crucial leadership enabled our struggle and bent the arc of history toward good," he said. The White House said in a press release, Biden "reiterated the U.S. commitment to support Ukraine's defense against Russian aggression for as long as it takes, and to hold Russia accountable for its actions." The statement continued, "On behalf of the American people, President Biden expressed his admiration for the bravery and sacrifice of the Ukrainian people fighting for their freedom and their secure future."

-ABC News' Ellie Kaufman & Molly Nagle

In light of the presumed death of Wagner Group leader Yevgeny Prigozhin, the Russian Volunteer Corps, a group of Russians fighting alongside the Ukrainian Armed Forces, released a video appealing to the PMC's members.

The statement offered them "a difficult but rather logical choice: either subjugate themselves to the Russian Ministry of Defense in the service of the killers of their commanders, or save their honor and take revenge on their executioners, going over to the side of Ukraine."

"If you have not committed war crimes on the territory of Ukraine, then we invite you to join our ranks," the statement said.

The wider Ukrainian military has not commented on the offer or whether any theoretical defections would in fact be supported.

-ABC News' Will Gretsky

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

Wagner Group leader Yevgency Prigozhin was "likely" killed in a plane crash near Kuzhenkino, Russia, on Wednesday, the Pentagon said.

Pentagon press secretary Brig. Gen. Pat Ryder said there is no information to suggest a surface-to-air missile brought down the plane. Nine others, including Wagner's co-founder, Dmitry Utkin, are also presumed dead.

"We don't have any information to indicate right now ... there was some type of surface to air missile that took down the plane ... we assessed that information to be inaccurate," Ryder said.

He added, "But beyond that, I'm really just not going to have any further information. What was it, something that came ... from inside the plane? Again, I don't have any additional insight to provide on that."

-ABC News’ Luis Martinez

Ukrainian Armed Forces have yet to reach their "full potential," but two top generals exclusively told ABC News the counteroffensive is "going to plan" despite concerns from Western analysts that Ukraine is not making enough progress.

Gen. Oleksandr Tarnavskyi, who is leading the counteroffensive in the south, told ABC News' chief global affairs correspondent Martha Raddatz that the situation is "stable."

"The main thing is that we haven’t reached our full potential," Tarnavskiy said.

Ukrainian troops launched the counteroffensive a month ago, attacking on multiple axes on the southern frontline in Zaporizhzia using Western-supplied vehicles. Ukraine succeeded in piercing Russian lines at two points, liberating a string of villages, but has since been locked in ferocious fighting

Gen. Oleksandr Syrskyi, commander of the Ukrainian ground forces, told Raddatz that last month's failed rebellion by the Putin-backed PMC, the Wagner Group, wouldn't impact the fighting on the ground.

"It would be better for us if there were some negative consequences in Russia itself, but it doesn't matter for me," he said.

Asked if he was confident of retaking the key city of Bakhmut, Syrskyi said, "Yes, of course. I’m sure."

Both sides have suffered heavy casualties, according to Western officials, particularly in the south where Russia has so far conducted "relatively effective defensive operations" in the southeastern Zaporizhzhia province, the U.K. Ministry of Defense reported.

"The enemy is suffering eight times or even 10 times higher losses, especially with the number of killed troops," Syrksyi said.

-ABC News' Guy Davies and Meghan Mistry