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

CIA Director Bill Burns said Yevgeny Prigozhin's mutiny showed the "corrosive effect" of President Vladimir Putin's war in Ukraine during remarks in England on Saturday.

"It is striking that Prigozhin preceded his actions with a scathing indictment of the Kremlin’s mendacious rationale for its invasion of Ukraine, and of the Russian military leadership’s conduct of the war," Burns said during a lecture to Britain's Ditchley Foundation. "The impact of those words and those actions will play out for some time, a vivid reminder of the corrosive effect of Putin’s war on his own society and his own regime."

Burns, who served as U.S. ambassador to Russia from 2005 to 2008, also noted how Russian disaffection will gnaw away at the Kremlin and that the CIA is taking this opportunity to step up its recruitment efforts in Russia.

"Disaffection with the war will continue to gnaw away at the Russian leadership, beneath the steady diet of state propaganda and practiced repression," Burns said. "That disaffection creates a once-in-a generation opportunity for us at CIA, at our core a human intelligence service. We're not letting it go to waste."

-ABC News' Cindy Smith