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

President Volodymyr Zelenskyy again called on Tuesday for NATO to invite Ukraine to become a member, offering a strongly worded statement as the coalition leaders gathered for a summit in Lithuania.

Ukraine "deserves respect," Zelenskyy said in a statement posted on Twitter.

"It's unprecedented and absurd when time frame is not set neither for the invitation nor for Ukraine's membership," he said. "While at the same time vague wording about 'conditions' is added even for inviting Ukraine. It seems there is no readiness neither to invite Ukraine to NATO nor to make it a member of the Alliance."

Keeping Ukraine out of NATO amounts to a "motivation" for Russia to "continue its terror," he said.

"Uncertainty is weakness," he added.

Russia rebutted the statement a short while later.

"This is potentially very dangerous for European security. Indeed, it is fraught with great dangers, and those who will make this decision should be aware of that," Dmitry Peskov, a Kremlin spokesperson, said when asked to comment on Ukraine's possible fast-track admission to the coalition.