Russia on Friday vehemently denied having any involvement in the mysterious plane crash that is believed to have killed Wagner Group leader Yevgeny Prigozhin.

"There has been a lot of speculation around this crash [and] the tragic deaths of the plane's passengers, among them Yevgeny Prigozhin. Of course, the West presents all this speculation from a particular angle. All of that is sheer lies," Kremlin spokesperson Dmitry Peskov told reporters while answering questions during a press briefing. "One should rely on facts. For now, there are not many facts, they have yet to be established in the ongoing investigative procedures."

Prigozhin, 62, was a former close ally of Russian President Vladimir Putin. His private paramilitary organization played a key role in Putin's invasion of neighboring Ukraine before briefly launching an insurrection against the Russian military in June. Forces loyal to Prigozhin marched toward Moscow before turning back after several days.

A private jet was en route from Moscow to St. Petersburg on Wednesday when it went down near the village of Kuzhenkino in Russia's Tver region, north of Moscow. All 10 people on board were killed. Prigozhin and Wagner Group co-founder Dmitry Utkin were among the passengers identified on a flight list, according to Russian officials.

The U.S. Department of Defense said Thursday that Prigozhin was "likely" killed in the plane crash.

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

The Ukrainian military has landed troops on the Russian-held eastern bank of the Dnipro River across from the city of Kherson, according to Russian reports.

Media posted online by pro-Russian accounts suggested small boatloads of Ukrainian soldiers have managed to establish a small beachhead at the foot of the destroyed Antonivskiy Road Bridge that spanned the river before Ukraine brought it down last year.

The size of the Ukrainian force on the bank is unclear, but Russian accounts suggested it was relatively small.

Some Russian accounts posted dramatic video showing fighting on the eastern bank, including what appears to be a Russian armored vehicle firing intensively at Ukrainian soldiers as it recovers Russian wounded.

The video was undated but Russian reports suggested around several dozen Ukrainian troops landed on June 24 and Russian airborne units have been trying to dislodge them since.

Another video shows a small boat carrying perhaps a dozen Ukrainian soldiers landing by the ruined bridge, coming under shell fire.

The Russian military blogger account, Two Majors, reported a small group of Ukrainian soldiers had succeeded in digging in around the bridge. It noted Russian forces had been forced to pull back to a distance from the bank because their positions had been flooded after the Kakhovka dam was blown up earlier this month.

Russian military bloggers said Russian aircraft and artillery were firing on the Ukrainians Monday.

If Ukraine is able to keep hold of its foothold, it will put further pressure on Russia’s forces in the south, already battling to hold back Ukraine’s counteroffensive on the Zaporizhzhia front.

-ABC News' Patrick Reevell