Russian oligarch Yevgeny Prigozhin, who runs the private military company Wagner, said Wednesday that Russia’s retreat from the key Ukrainian city of Kherson was painful but necessary.

Prigozhin, nicknamed "Putin's Chef" due to his restaurant and catering businesses, said Russian troops had to withdraw from Kherson because they were nearly surrounded by Ukrainian forces and cut off from supply lines.

“Neither I, nor Wagner abandoned Kherson," Pigozhin said. "Without question, it is not a victorious step in this war, but it’s important not to agonize, nor to fall into paranoia, but to make conclusions and work on mistakes."

He praised Russian Gen. Sergey Surovikin for making the decision to withdraw Russian troops and saving the lives of thousands of soldiers.

-ABC News' Patrick Reevell

Russia’s defense minister and top commander in Ukraine announced Wednesday that Russian troops will pull back from the key city of Kherson in southern Ukraine.

Defense minister Sergey Shoigu said he accepted a proposal from Russian Gen. Sergey Surovikin to order Russian forces to retreat to the eastern bank of the Dnieper River, in effect abandoning the city of Kherson.

Surovikin said it was a “very difficult decision” and justified it as necessary to save the lives of Russian soldiers and to preserve their capacity for future operations.

“Besides that, it frees up part of the forces and resources, which will be employed for active actions, including offensive, in other directions,” Surovikin said in the televised meeting with Shoigu.

Kherson is the only regional capital the Russians have occupied since 2014. The city and the surrounding area act as a gateway to Crimea Peninsula, which was annexed by Russia in 2014.

Brittney Griner, the WNBA star detained in Russia, has been transferred to a penal colony, a move decried by White House officials.

"Every minute that Brittney Griner must endure wrongful detention in Russia is a minute too long," White House press secretary Karine Jean-Pierre said in a statement early Wednesday. "As the Administration continues to work tirelessly to secure her release, the President has directed the Administration to prevail on her Russian captors to improve her treatment and the conditions she may be forced to endure in a penal colony."

Griner's lawyers said in a statement that she was transferred on Nov. 4 from a detention center in Iksha. She's now on her way to a penal colony in an undisclosed location.

"We do not have any information on her exact current location or her final destination," the lawyers, Blagovolina and Alexander Boykov, said in a statement. "In accordance with the standard Russian procedure the attorneys, as well as the U.S. Embassy, should be notified upon her arrival at her destination."

The White House said it had made a "significant offer" to Russian officials to "resolve the current unacceptable and wrongful detentions of American citizens."

"In the subsequent weeks, despite a lack of good faith negotiation by the Russians, the U.S. Government has continued to follow up on that offer and propose alternative potential ways forward with the Russians through all available channels," Jean-Pierre said in a statement.

She added, "The U.S. Government is unwavering in its commitment to its work on behalf of Brittney and other Americans detained in Russia -- including fellow wrongful detainee Paul Whelan."

-ABC News' Cindy Smith, Ahmad Hemingway and Tanya Stukalova

Moscow is closely "following" the midterm elections in the United States and knows that some Republican candidates have proposed to cut the country's military aid to Ukraine, according to Russian Deputy Foreign Minister Alexander Grushko.

"Naturally, we are following the developments in the United States," Grushko said in an interview with Russian state-owned television network Zvezda on Tuesday. "We are aware that a number of prominent Republicans favor reducing the military assistance to Ukraine, because they proceed from the position that what Democrats are currently doing is irrational."

If Republicans are triumphant, Grushko said, the U.S. Congress could ramp up pressure on European nations regarding their defense budgets.

"We remember that one of [former U.S. President Donald] Trump's key slogans when he came to power was that the Europeans should pay for their defense themselves," he added. "Largely thanks to his efforts, European countries took enhanced commitments to increase their defense budgets to 2%. And there have been talks that defense spending should now reach at least 3%. The United States will continue to pursue the policy it has been running since 1949."

Federal agents searched the New York City apartment of Russian billionaire Viktor Vekselberg on Thursday, law enforcement sources told ABC News.

The oligarch's Park Avenue apartment was searched by federal agents with the FBI and Homeland Security Investigations, the main investigative arm of the U.S. Department of Homeland Security, the sources said.

An address in East Hampton associated with Vekselberg is also being searched as part of court-authorized activity involving the Justice Department's KleptoCapture task force, according to sources.

The task force has been seizing assets of Russian businessmen associated with Russian President Vladimir Putin over suspected violations of U.S. sanctions following the invasion of Ukraine.

The task force is trying to find yachts, airplanes and other moveable property before the oligarchs can transport them to jurisdictions where it might be more difficult for U.S. authorities to investigate.

In April, Spanish authorities seized Vekselberg's $90 million yacht in the port of Palma de Mallorca at the request of the Justice Department.

Vekselberg was among the oligarchs previously sanctioned by the U.S. after Russia invaded Crimea in 2018.

-ABC News' Aaron Katersky