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

Mykhailo Podolyak, an adviser to the office of Ukrainian President Volodymyr Zelenskyy and the lead negotiator in Ukraine-Russia talks, is urging world leaders to take a stance on the conflict Russia has sparked in Ukraine, saying the third world war is already among us.

"It’s already World War III –- world leaders must now choose their side," Podolyak told ABC News. "Every leader of every country must explain why he will stand to the side at the time when Russia was shelling civilian children in Ukraine."

Podolyak is "cautiously optimistic" that negotiations are progressing, he said, adding that Ukraine will not offer any concessions to Russia.

"My cautious optimism is based on the fact that they understand they will not break us and they will not have enough resources to answer what they started," he said.

Podolyak said that, despite what he described as "Russian propaganda" reports, no foreign fighters were killed during the strike on Yavoriv, on the outskirts of Lviv, on Sunday. He accused Russia of using the ceasefire -- which was implemented to establish humanitarian corridors -- to regroup and reposition themselves for strategic attacks.

In addition, the bombing and shelling of civilians in Southern Ukraine continues to intensify, Podolyak said.

More negotiations between Ukraine and Russia are schedule to take place tomorrow, Podolyak said.

-ABC News' Maggie Rulli

The United Nations High Commissioner for Refugees has calculated that 2,698,280 people have fled Ukraine since Feb. 24 as a result of the Russian invasion.

About 1.66 million people have entered Poland, 246,206 people have entered Hungary, and 195,980 people have entered Slovakia.

Nearly 200,000 people have entered Russia, Moldova, Romania and Belarus combined, while more than 304,000 people have entered other European countries.

-ABC News' Zoe Magee

The International Committee of the Red Cross is calling for an urgent solution for the "life-and-death" situation facing the hundreds of thousands of civilians trapped in Mariupol without access to running water and electricity as the heavy airstrikes from Russian forces continue.

A "worst-case" scenario awaits those who remain in the city unless a humanitarian agreement among the fighting parties is reached immediately, the ICRC said in a press release on Sunday.

"We call on all parties involved in the fighting to place humanitarian imperatives first. People in Mariupol have endured a weekslong life-and-death nightmare. This needs to stop now," Peter Maurer, president of the ICRC, said in a statement. "Their safety and their access to food, water and shelter must be guaranteed."

People of all ages, including Red Cross staff, are sheltering in unheated basements and risking their lives to make short runs outside for food and water, according to the ICRC.

Dead bodies, both of civilians and combatants, remain trapped under the rubble or lying in the open where they fell, and those suffering injuries or chronic, debilitating conditions are unable to seek treatment.

"The sound of warfare is constant. Buildings are struck, and shrapnel flies everywhere," said ICRC's operational leader in Mariupol, Sasha Volkov. "This is the situation every person in the city faces."

-ABC News' Zoe Magee

An American who traveled to Ukraine to assist in the country's stand against the Russian invasion described the heavy bombardment parts of western Ukraine are now seeing.

Glock Dara, 29, was asleep at the military training ground in Yavoric, on the outskirts of Lviv, when he heard the first missiles begin to strike on Sunday morning.

"I didn’t have time to panic. I just focused on running as fast as I can," Dara told ABC News. "Hella chaos, bombs falling left and right -- you’re just praying to God it doesn’t happen to you."

The strikes left at least 35 dead and 134 wounded, according to Ukrainian officials. Russian officials claim 180 foreign mercenaries are dead.

Dara is one of roughly two dozen soldiers evacuated from Yavoriv and brought to the Korczowa refugee center in Poland Sunday afternoon, about 15 miles away.

All of the men ABC News spoke with at the refugee center were volunteer foreign fighters from Ireland, France, Boston -- most dressed in uniforms bearing the Ukrainian flag. The base served as a launching pad for foreign fighters who were trained there and then deployed across the country, one medic from Ireland told ABC News.

"A lot" of Americans are at the American base as well, Dara said. He and some of the men he travelled with are now planning to re-group in Krakow, but Dara already intends to back to Lviv, he said.

"I came here as a volunteer counter-terrorist," he added.

The Korczowa refugee center has already seen a significant increase in the number of people coming in from western Ukraine in just the last couple days, volunteers at the shelter told ABC News.

-ABC News' Ines De La Cuerta