Russia-Ukraine updates: 2 US veterans who joined Ukrainian forces missing

Russian President Vladimir Putin declared on Thursday that his siege of Mariupol had been a success, congratulating his defense minister and thanking Russian troops.

"The completion of the combat work to liberate Mariupol is a success," Putin said. “I congratulate you. Convey words of gratitude to the troops."

Putin’s claim of victory came as he ordered troops to abandon their assault on the Azovstal Iron and Steel Works plant, the last holdout for Ukrainian troops in the port city.

A Ukrainian commander of the regiment at the site said Ukrainian troops there are ready to surrender, if their safety can be guaranteed by a third party and they are allowed to take the bodies of their dead with them.

Ukrainian President Volodymyr Zelenskyy's office called for negotiations inside Mariupol to get anyone left in the factory out of the area alive.

At a news conference Thursday, President Joe Biden pushed back on Putin's claim that Russia has control over Mariupol.

"There is no evidence yet that Mariupol has completely fallen," Biden said.

-ABC News’ Tanya Stukalova, Iryna Hnatiuk, Molly Nagle and Yulia Drozd

President Joe Biden on Thursday announced a new $800 million security assistance package to help Ukrainians fighting in the eastern Donbas region. This funding includes heavy artillery weapons, tactical drones and howitzers.

This package includes 72 new howitzers. Combined with the 18 howitzers announced last week, the 90 howitzers headed to Ukraine can equip five battalions, according to the administration.

Biden noted that he’s run out of pre-approved money and equipment to send to Ukraine and he appealed to Congress to approve more.

When pressed by ABC News on how long the U.S. can sustain this level of spending, Biden said, “We have the capacity to do this for a long time."

He went on, "The question is, are we going to continue to maintain the support of the international community? And keep the pressure on Putin to prevent him from overrunning the country, No. 1, and No. 2, make sure we continue to maintain the economic sanctions, which, over time, and we're beginning to see, they’re devastating their economy and their ability to move forward."

Biden also announced a separate $500 million in economic aid to Ukraine to help fund government operations like salaries, pensions and social programs.

The president added that the U.S. is now banning Russian-affiliated ships from American ports.

Biden met with Ukrainian Prime Minister Denys Shmyhal Thursday morning ahead of his remarks.

-ABC News' Luis Martinez and Sarah Kolinovsky

The Biden administration on Thursday is moving to fast-track Ukrainian refugees trying to come to the U.S. with an operation called "Uniting for Ukraine."

Beginning April 25, U.S. based individuals and entities can apply to the Department of Homeland Security to sponsor Ukrainian citizens, the administration said.

Any U.S. citizen or entity can apply to sponsor Ukrainians and there's no limit on how many Ukrainians a person or entity can sponsor, administration officials said. A background check is required.

Any Ukrainian who has been a resident of the country since Feb. 11 and has up-to-date vaccinations will be eligible for the program. They will be subject to a background check, biometric screening and other security checks.

Ukrainians who don't have a visa to enter the U.S. will be encouraged to apply for this program.

Administration officials said this was part of President Joe Biden's promise to take in 100,000 Ukrainians into the U.S.

For those who don't have sponsors or friends or family in the U.S., the administration is working with non-governmental organizations and nonprofit organizations to help connect people to them.

"One of the reasons we are having sponsors that are entity based … is precisely to deal with those situations," one administration official said.

In addition to this new program, officials said the State Department will expand resettlement operations in Europe for Ukrainian citizens.

-ABC News' Luke Barr

Russian President Vladimir Putin canceled his military's attack on a Mariupol steel plant, one of the last areas in the port city held by Ukrainian forces, ordering his troops to instead seal all exit routes from the sprawling plant.

“I consider the proposed assault on the industrial zone impractical,” Putin told Sergei Shoigu, his defense minister, during a meeting televised on Thursday by Russian state media, according to a translation of the Kremlin’s official transcript.

The Mariupol city council claimed Tuesday that there are at least 1,000 civilians, mostly women with children and the elderly, seeking shelter in the Azovstal Steel and Iron Works plant. It was unclear how many Ukrainian troops were defending the site.

Putin in the televised meeting ordered his troops to “block” the industrial zone. He repeated the claim that Moscow would let troops leave unharmed if they lay down their weapons and surrender.

“There is no need to climb into these catacombs and crawl underground on these industrial facilities," Putin said. "Block this industrial area so that the fly does not fly."