Russian President Vladimir Putin met with Wagner Group leader Yevgeny Prigozhin days after the rogue paramilitary leader launched a failed uprising, the Kremlin said on Monday.

The June 29 meeting came about a week after the rebellion failed, Kremlin spokesman Dmitry Peskov said.

"Indeed, the president had such a meeting, he invited 35 people to it -- all the commanders of the detachments and the management of the company, including Prigozhin himself," Peskov said Monday, according to Interfax, a Russian newswire. "This meeting took place in the Kremlin on June 29, it lasted almost three hours."

-ABC News' Anastasia Bagaeva and Joe Simonetti

At least eight people are dead and 13 others are injured after a Russian rocket struck the Ukrainian town of Lyman in the Donetsk Region on Saturday morning, according to the head of the regional military administration, Pavlo Kyrylenko.

The attack struck a neighborhood with private residences, damaging a home and a store.

As of Kyrylenko's update, police and paramedics were still on site to provide necessary medical assistance.

-ABC News' Tatyana Rymarenko

Russian shelling on the town of Pervomayskyi, located in the region of Kharkiv, has injured 43 people, including 12 children, Oleh Synyehubov, the head of the Kharkiv Regional State Administration, said .

A residential building was damaged and multiple cars were destroyed in the shelling, according to Synyehubov.

-ABC News' Fidel Pavlenko

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

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