Russian President Vladimir Putin's comments Thursday morning claiming victory in Mariupol was "yet more disinformation" from Russia's "well-worn playbook," State Department spokesperson Ned Price told reporters.

Price called Putin's comments an attempt to "distract from what can only be considered the underperformance of Russia's military forces and its failure to achieve its original objectives in Ukraine."

Price said Ukrainian forces in Mariupol "continue to hold their ground."

"Their ferocious stand stands in stark contrast to the plummeting morale that we've seen among Russia's forces. It stands in stark contrast to the tactics that we've seen Russia impose against those in Mariupol," he added.

Price said the U.S. has called for humanitarian access -- aid to get in and people to get out -- and has supported humanitarian groups working to do so. But he blamed Russia's attacks on humanitarian corridors for preventing it from happening.

-ABC News' Conor Finnegan

The U.S. has assessed that the Ukrainian port city of Mariupol remains contested, and that Russian airstrike activity remains focused there and on the Donbas region, a senior U.S. defense official said Thursday.

Russia now has 85 battalion tactical groups, each made up of roughly 800 to 1,000 troops, inside of Ukraine, the official said. More of these groups are headed to the Donbas region, the official said.

-ABC News' Luis Martinez

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

Mariupol has not yet fallen, despite Russia's demands that Ukrainian troops defending the besieged Ukrainian port city surrender, according to Ukrainian Prime Minister Denys Shmyhal.

"There [are] still our military forces, our soldiers, so they will fight until the end," Shmyhal told ABC News' George Stephanopoulos in an exclusive interview Sunday on "This Week."

Mariupol is a strategic city for Moscow because it would allow Russian forces in the south to connect with troops in eastern Ukraine's contested Donbas region. It would also give Moscow a key port.

Although Mariupol remains under the Ukrainian government's control, Shmyhal said the city's residents are suffering.

"They have no water, no food, no heat, no electricity," he said. "They ask all of our partners to support and help stop this humanitarian catastrophe."

-ABC News' Monica Dunn