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

Ukrainian President Volodymyr Zelenskyy and U.S. President Joe Biden are set to meet in Lithuania’s capital on Wednesday afternoon, a day after NATO leaders announced during a summit that Ukraine will be allowed to join the alliance "when allies agree and conditions are met" but didn't offer a timeline.

Earlier Wednesday, Zelenskyy held a joint press conference with NATO Secretary-General Jens Stoltenberg, fielding many questions from reporters about Ukraine's path to NATO membership. The Ukrainian president took a noticeably softer tone compared to his remarks the previous day criticizing the lack of a timeline as "unprecedented and absurd."

Zelenskyy told reporters it's difficult as NATO partners are living under different conditions, whereas in Ukraine "survival" matters. He said he understands some people are "afraid" to talk about Ukraine joining NATO because "nobody is willing to have a world war." He acknowledged that his country cannot be a member of the alliance while a war is going on within its borders, but he said "signals are important."

When asked about his upcoming meeting with Biden and how he plans to convince the U.S. president that Ukraine is ready for NATO membership, Zelenskyy responded with gratitude to the United States and confidence that Ukraine will join the alliance once Russia's war is over.

"I'm grateful to President Biden and to the Congress and to the people of United States that are truly the leaders in support and assistance to Ukraine. We highly appreciate this," the Ukrainian president told reporters. "Not planning to find any arguments for making sure that President Biden would see us in NATO. I believe that those arguments, they should be mutual because it's all about this security, the East, the European continent, the Eastern Flank of NATO. And I believe that NATO needs us just as we need NATO. And I believe that this is absolutely fair. I am confident that after the war, Ukraine will be in NATO. We will be doing everything possible to make it happen so that we with the United States would have a same understanding and same vision."

-ABC News' Molly Nagle and Joe Simonetti