Russia claimed Wednesday that more than a thousand Ukrainian soldiers had surrendered in Mariupol, a besieged port city in southeastern Ukraine that is still held by Ukrainian forces.

"In Mariupol city, near the 'Illich' Steelworks, 1,026 Ukrainian servicemen of the 36th Marine Brigade have voluntarily laid down their arms and surrendered as a result of a successful offensive by the Russian Armed Forces and Donetsk People's Republic militia units," the Russian Ministry of Defense said in a statement.

The surrendering troops included 162 officers and 47 women, according to the ministry.

"151 wounded Ukrainian servicemen of the 36th Marine Brigade received primary medical care immediately on the spot, after that they were all taken to the Mariupol city hospital for further treatment," the ministry added.

The Biden administration could announce as early as Wednesday upward of $750 million in additional military assistance to Ukraine, a U.S. official told ABC News.

The new assistance could possibly include a range of military hardware -- including howitzers, artillery and Humvees -- though the full package still needs to be finalized, the official said.

-ABC News' Luis Martinez

Correction: Mi-17 helicopters are not being considered as part of the package, as previously reported.

President Joe Biden used the word "genocide" for the first time to describe Russia's actions in Ukraine during remarks on Tuesday.

"Your family budget, your ability to fill up your tank -- none of it should on hinge on whether a dictator declares war and commits genocide half a world away," Biden said in Menlo, Iowa, during remarks primarily about the U.S. economy.

Biden was asked by reporters on April 4 if he thought the atrocities in Bucha were a genocide, as Ukrainian President Volodymyr Zelenskyy had claimed. "No, I think it is a war crime," Biden responded then.

That same day, Biden's national security adviser, Jake Sullivan, said the administration had not yet seen the "systematic deprivation of life" necessary to meet the definition of genocide.

Biden confirmed his word choice to the White House pool Tuesday evening before boarding Air Force One, saying that since last week the "evidence is mounting."

"Yes, I called it genocide," Biden said. "Because it has become clearer and clearer that Putin is just trying to wipe out the idea of even being able to be a Ukrainian."

He then qualified that the determination of genocide is officially up to legal experts, but that "it sure seems that way to me."

-ABC News' Sarah Kolinovsky

The U.S. State Department is condemning the arrest in Russia of Vladimir Kara-Murza, a Russian opposition activist and critic of the Kremlin's invasion of Ukraine.

State Department spokesperson Ned Price said Kara-Murza's arrest on Monday is another example of a Russian government "that is more aggressive beyond its borders and more oppressive within its borders."

He condemned Kara-Murza's arrest, noting that the activist has previously been arrested by Russian authorities and that he has survived two poisoning incidents.

"The Russian people -- and this is the key point -- like people everywhere, have the right to speak freely, to form peaceful associations, to exercise their freedom of expression and to have their voices heard through free and fair elections," Price said.

Kara-Murza, a Washington Post columnist who has testified before Congress, survived poisoning incidents in 2015 and in 2017. At the time of his second poisoning, Kara-Murza's wife, Evgenia Kara-Murza, gave an exclusive interview to ABC News in which she pleaded for then-President Donald Trump to support her husband and warned that Putin "cannot be dealt with on friendly terms."

Following her husband's arrest this week, Evgenia Kara-Murza posted a message on Twitter calling attention to her husband's arrest.

"Twice have the Russian authorities tried to kill my husband for advocating for sanctions against thieves and murderers, and now they want to throw him in prison for calling their bloody war a WAR. I demand my husband's immediate release!" Evgenia Kara-Murza, who lives in the Washington, D.C., area, tweeted.

-ABC News' Conor Finnegan

White House national security advisor Jake Sullivan hinted Thursday of more sanctions coming against Russia in the "next week or two" aimed at targeting ways Moscow is evading sanctions already imposed.

“Where our focus will be over the course of the coming days is on evasion,” Sullivan said Thursday at the Economic Club of Washington. “As Russia tries to adjust to the fact that it’s under this massive economic pressure, what steps do they take to try to evade our sanctions and how do we crack down on that? And I think we'll have some announcements in the next week or two that identify targets that are trying to facilitate that evasion both inside Russia and beyond."

When Sullivan was asked whether sanctions will automatically be lifted if a negotiated peace deal between Russia and Ukraine is worked out, he appeared cautious with his words, saying, “a lot of that depends on what the shape and scope” of the agreement is.

“A lot of it depends on what the Ukrainians, in consultation with us and the Europeans come to agree to," Sullivan said. "You know, we're not going to do a deal over the head of the Ukrainians where we give a bunch of sanctions relief to Russia. But if some measure of sanctions relief were built in to some credible diplomatic solution led by the Ukrainians, that's something that we would happily discuss."

But Sullivan said Russian oligarchs shouldn't expect to ever get back their yachts and other assets seized under sanctions that have been imposed, saying the ultimate goal is "not to give them back” once the war is over.

“The president is actively looking at how we can deal with the fact that as we seize these assets, our goal is not to give them back. Our goal is to put them to a better use than that," Sullivan said. "But I'll be careful in what I say today because there's an ongoing kind of policy process around how we end up dealing with that question. But, rest assured, that the goal is not just to sit on them for a while."

-ABC News' Justin Gomez