Ukraine has recaptured approximately 300 square kilometers during the summer counteroffensive so far, United Kingdom Defense Secretary Ben Wallace said Tuesday.

The gains represent more territory than Russia seized during its winter offensive in 2022, Wallace told Parliament.

-ABC News' Ellie Kaufman

Belarus President Alexander Lukashenko provided more details about his alleged role in negotiations between Wager Group leader's Yevgeny Prigozhin and Russian President Vladimir Putin following the PMC's rebellion.

Lukashenko claimed Prigozhin abandoned his demands, including the resignation of Shoigu, after they talked.

"[Prigozhin] told me 'Alexander Grigoryevich, I will not demand from the president that he give up Shoigu and Gerasimov, and I will not even ask for a meeting,' I say, 'Well, that’s good. This is a very good move,'" Lukashenko claimed.

Lukashenko said that Wagner forces could join the Belarusian army but said that he won't built camps for Wagner's troops in his country.

"We don't need to open any Wagner recruitment points," he said.

-ABC News' Victoria Beaule

Belarus President Alexander Lukashenko said on state media Tuesday that Wagner Group leader Yevgeny Prigozhin arrived in his country earlier in the day.

Lukashenko claimed on state media that "security guarantees" Russian President Vladimir Putin promised to Prigozhin were provided.

"Yes, indeed, he is in Belarus today. As I promised, if you want to stay with us for a while and so on, we will help you," Lukashenko said.

A senior U.S. official confirmed to ABC News that Prigozhin is in exile in Belarus, surrounded by a security force of his own Wagner mercenaries.

-ABC News' Victoria Beaule, Tanya Stukalova and Martha Raddatz

Ukrainian troops have reportedly seized a small village on the Russian-occupied eastern bank of Dneipr after crossing the river from the liberated city of Kherson, according to Russian accounts on Tuesday.

A small Ukrainian force has managed to dig in to the village of Dachi after making a landing there a few days ago and are trying to expand the beachhead. Ukrainian troops in small boats crossed the river and landed at the base of the ruined Antonivskiy Bridge, which they destroyed last year.

Russian military bloggers reported very heavy fighting on Tuesday, saying Russian airborne units have been trying unsuccessfully to dislodge the Ukrainians for the past four days. Russian aviation and heavy artillery have been firing on the Ukrainian position.

So far, the Russian side claims some 70 Ukrainian soldiers are dug in, covered by intense artillery fire from across the river. The Russian accounts say Ukraine is trying to move reinforcements across. Video released by Ukraine also shows a Russian APC being destroyed in the village of Oleshkjy, further south, indicating the bank south of Kherson is now contested.

Ukrainian troops have also managed to advance and liberate Rivnopil, a village on the Zaporozhzhia front, breaking through after more than two weeks of fighting. It's notable because the Russians had been fighting hard to hold it.

Taken together the advance there, the landing in Kherson and advances near Bakhmut are small signs the Ukrainian counteroffensive may be starting to pick up steam and the Russians are coming under growing pressure.

-ABC News' Patrick Reevell

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