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

In the wake of Saturday's short-lived attempted rebellion against the Kremlin by the Wagner private military company, Mikhail Khodorkovsky, an exiled oligarch considered one of Putin’s best-known opponents, told ABC News he supports the mutiny and encourages Russians to back the leader of the mercenary group.

Once Russia’s richest man, Khodorkovsky, a Putin opposition activist, spent 10 years imprisoned after he challenged Putin, his case now considered a foundational moment for Putin’s regime.

When Wagner founder Yevgeny Prigozhin and his fighters marched on Moscow Saturday before making a sudden about-face, Khodorkovsky was notable among Russia’s pro-democracy opposition in calling on people to support Prigozhin, arguing that allowing him to remove Putin would create an opportunity for the democrats.

Khodorkovsky told ABC News he believed Prigozhin’s actions were a real coup attempt and that it had “seriously undermined” Putin’s power. He predicted that similar opportunities to collapse the regime will be launched soon.

"The blow to Putin’s reputation, to the authorities’ reputation, was absolutely fantastical," Khodorkovsky said. "Putin’s government today is, without a doubt, strongly undermined by what happened -- his authority, his ability to control the security services is seriously undermined."

Khodorkovsky said Prigozhin’s march on Moscow had undermined Putin’s popularity, showing neither ordinary Russians nor the security services were prepared to act to protect him.

“Along the entire route of Wagner's columns, no one in any way tried to hinder him (Prigozhin). Even the security forces did not try to stop him," Khodorkovsky said. “It showed that, in fact, inside the country, Putin has an absolute void."

Khodorkovsky said he did not support Prigozhin himself -- considering him a "war criminal" -- but that the democratic opposition should have sought to help him overthrow Putin, and then taken power from him after.

Khodorkovsky criticized other parts of the anti-Kremlin opposition who attacked him for calling on people to assist Prigozhin, saying he believed the opposition had “slept through” the opportunity and suggesting it should have sought to stage a rebellion in Moscow at the same time.

"There will definitely now be more such opportunities because of Putin’s weakening. But the next time we need to simply be more ready," said Khodorkovsky, who is living in exile in England. "If an uprising had started in Moscow to meet Prigozhin then a situation could have developed quite differently.

ABC News' Patrick Reevell