Wagner Group leader Yevgeny Prigozhin released an 11-minute recording Monday explaining why his troops reversed course on their campaign against Moscow over the weekend.

Prigozhin said the purpose of the "march" was to prevent losses of his troops "and to bring justice to all persons who, through their unprofessional actions, made a huge number of mistakes during" the war in Ukraine.

"We had no goal of overthrowing the regime," he added, referring to Putin's government.

Prigozhin said that the march escalated after their convoy was hit by a missile attack from Russian forces.

Prigozhin said that the marched stopped when his troops approached "Moscow deployed artillery."

"We did not want to shed Russian blood. We went to demonstrate our protest and not to overthrow the government in the country," he said.

He claimed that several of his troops were wounded and two were killed.

-ABC News' Ellie Kaufman, Natalia Shumskaia and Tanya Stukalova

The Ukrainian military has landed troops on the Russian-held eastern bank of the Dnipro River across from the city of Kherson, according to Russian reports.

Media posted online by pro-Russian accounts suggested small boatloads of Ukrainian soldiers have managed to establish a small beachhead at the foot of the destroyed Antonivskiy Road Bridge that spanned the river before Ukraine brought it down last year.

The size of the Ukrainian force on the bank is unclear, but Russian accounts suggested it was relatively small.

Some Russian accounts posted dramatic video showing fighting on the eastern bank, including what appears to be a Russian armored vehicle firing intensively at Ukrainian soldiers as it recovers Russian wounded.

The video was undated but Russian reports suggested around several dozen Ukrainian troops landed on June 24 and Russian airborne units have been trying to dislodge them since.

Another video shows a small boat carrying perhaps a dozen Ukrainian soldiers landing by the ruined bridge, coming under shell fire.

The Russian military blogger account, Two Majors, reported a small group of Ukrainian soldiers had succeeded in digging in around the bridge. It noted Russian forces had been forced to pull back to a distance from the bank because their positions had been flooded after the Kakhovka dam was blown up earlier this month.

Russian military bloggers said Russian aircraft and artillery were firing on the Ukrainians Monday.

If Ukraine is able to keep hold of its foothold, it will put further pressure on Russia’s forces in the south, already battling to hold back Ukraine’s counteroffensive on the Zaporizhzhia front.

-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

Travel restrictions remained in place on Sunday on the major M-4 highway near Moscow, according to Russia’s state-run media.

"According to the previously issued regional decisions, traffic restrictions remain in force on the M-4 Don highway near the Moscow Region and the Tula Region," the federal road agency said, according to TASS.

The security checkpoints had been put in place Saturday as a column of Wagner Group forces traveled toward Moscow. Roadblocks in southern Russia, including in Rostov-on-Don and the Krasnodar Region, were reportedly lifted.

"All previously imposed restrictions on highways have been lifted," TASS reported, citing a branch of the Russian Interior Ministry.

-ABC News' KJ Edelman

The United States "is prepared to defend every inch of NATO territory," National Security Advisor Jake Sullivan said Wednesday, amid Russia's threats of military retaliation if Sweden and Ukraine officially join the alliance.

"At the end of the day, Russia does not get a vote in who joins NATO," Sullivan told ABC News' George Stephanopoulos during an interview Wednesday on "Good Morning America."

"If Russia does choose to test Article 5, President Biden has said he is prepared to defend every inch of NATO territory," he added. "And later tonight, when he addresses a large crowd in Vilnius in a speech about his vision for Euro-Atlantic security and for American leadership, he will reinforce this point about the sanctity of Article 5."

Article 5 of the NATO treaty states that the signed parties "agree that an armed attack against one or more of them in Europe or North America shall be considered an attack against them all."

Sweden and Finland, which have historically embraced neutrality, applied for NATO membership together last year despite warnings from Moscow against doing so, as Russian forces invaded Ukraine. Finland officially joined the alliance in April following Turkish ratification, but Turkey and Hungary have yet to ratify Sweden’s membership. NATO Secretary-General Jens Stoltenberg announced Monday that Turkish President Recep Tayyip Erdogan has agreed to send Sweden’s NATO accession documents to Turkey’s Parliament for approval "as soon as possible," one of the last steps in the membership process.

Meanwhile, Ukraine is pushing hard for NATO membership as Russia’s war presses on. Stoltenberg announced Tuesday that the bloc "will issue an invitation for Ukraine to join NATO when allies agree and conditions are met," pledging to speed up the process by eliminating bureaucratic hurdles, but without offering a timeline.

"All 31 allies got together yesterday to say with one voice that Ukraine's future is in NATO. The real question is just how we work down the pathway to get them in," Sullivan told ABC News on Wednesday. "So the signal that NATO sent yesterday was very positive to Ukraine about its future prospects for joining NATO, and we will work in terms of the democratic and security sector reforms that are necessary. And in the meantime, we're not just going to sit around. We're going to provide Ukraine with the weapons and military assistance it needs to defend its territory against Russia and to deter future aggression from Russia."

Ukraine has requested F-16 fighter jets and long-range missiles to aid its counteroffensive against Russian forces. Sullivan said the U.S. has already taken steps with NATO allies to begin the training of Ukrainian pilots on F-16s, which "will take some time," and then the aircraft will be transferred to Ukraine "likely from European countries that have excess F-16 supplies." As for the long-range missiles, Sullivan said the U.S. will continue to look into the issue and discuss it with Ukraine.