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

Mariupol Mayor Vadym Boychenko told ABC News he thinks his city will hold out, saying Russian forces have "been fighting our boys for 57 days and they still can’t win."

The mayor's comments come hours after Russian President Vladimir Putin declared that his siege of Mariupol had been a success, congratulating his defense minister and thanking Russian troops. Putin also ordered troops to abandon their assault on the Azovstal Iron and Steel Works plant, the last holdout for Ukrainian troops in the port city.

Boychenko said 100,00 civilians remain, including 1,000 in the steel plant.

President Joe Biden also pushed back on Putin's claim that Russia has control over Mariupol, saying at a news conference Thursday, "There is no evidence yet that Mariupol has completely fallen."

-ABC News' James Longman

Ukrainian Deputy Prime Minister Iryna Vereshchuk said 19 Ukrainians, 10 military and nine civilians, have been released from Russian captivity in the second prisoner swap this week.

-ABC News' Alexandra Faul

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