Russia-Ukraine updates: US sanctions Russian military shipbuilder, diamond miner

After meeting with the prime ministers of Poland, the Czech Republic and Slovenia in Kyiv on Tuesday, Ukrainian President Volodymyr Zelenskyy said that the European Union leaders took a "courageous, right" step.

"They are not afraid of anything. And they are more afraid for our fate. And they are here to support us," Zelenskyy said in a video posted to Facebook.

"We absolutely trust these friendly countries," he later said.

The leaders -- Czech Prime Minister Petr Fiala, Slovenian Prime Minister Janez Jansa and Polish Prime Minister Mateusz Morawiecki, as well as Polish Deputy Prime Minister Jaroslaw Kaczynski -- traveled to the Ukrainian capital on a European Union mission to show support for the country.

In another video, Zelenskyy said their visit was a "strong sign of support."

The meeting's "top agenda" was "international assistance and reconstruction of Ukraine," according to Ukrainian Prime Minister Denys Shmyhal.

The leaders are working together “to ensure that the funds & property of the Russian Federation will be paid to Ukraine to restore everything destroyed by [the Russian] aggressor," he said on Twitter.

-ABC News' Matt Foster

The U.S. will provide an additional $186 million in humanitarian assistance to support Ukrainians displaced by the war, including those in the country and refugees who have fled, Secretary of State Antony Blinken announced Tuesday.

The funding, which brings the total U.S. assistance since the invasion began to $293 million, will support "food, safe drinking water, protection, accessible shelter and emergency health care," he said in a statement.

The U.S. State Department and the U.S. Agency for International Development are not directly providing this assistance but are working through international and nongovernmental partners.

Russian bombardment and shelling continue to damage roads, bridges and railroads in Ukraine, making it difficult for aid workers to reach people in need, according to a senior administration official, who warned the situation is "rapidly getting worse."

-ABC News' Conor Finnegan

A pause in Russian attacks on the besieged city of Mariupol has allowed for around 20,000 people to evacuate after almost two weeks of continuous bombardment, Ukrainian authorities said.

About 4,000 private vehicles were able to get civilians out of the city on Tuesday, according to Kirilo Timoshenko, an official from Ukraine’s presidential office. Of those, around 570 have reached the safer city of Zaporizhzhia to the north.

This is in addition to the 160 private vehicles that evacuated residents during a lull on Monday.

Some 300,000 people had been estimated to be trapped in the city. Russian attacks impeded previous efforts to get civilians out and to allow for humanitarian supplies to be brought in.

The Mariupol City Council reported Sunday that 2,187 residents had been killed since the start of the invasion. Vereschuk said last week that the city was "beyond a humanitarian disaster," with most roads destroyed, little communication with the outside and no power, gas or heat.

The fourth round of talks between Ukrainian and Russian leaders will resume on Wednesday, Ukraine's presidential adviser Mykhailo Podolyak tweeted.

Podolyak called it a "very difficult" process with "fundamental contradictions," but added, "there is certainly room for compromise."

State Department spokesperson Ned Price on Tuesday declined to say whether the department was optimistic about the talks, but said the U.S. hasn't seen any action from the Kremlin to demonstrate "good faith."

"We have yet to find a Russian interlocutor that is either able or willing to negotiate in good faith, and certainly not in the context of de-escalation," he said.

-ABC News' Conor Finnegan and Christine Theodorou