European Commission President Ursula von der Leyen met with Ukrainian President Volodymyr Zelenskyy in Kyiv Saturday to discuss his country's bid to get candidacy status to join the European Union.

"The discussions today will enable us to finalize our assessment by the end of next week," von der Leyen said in a joint press conference with Zelenskyy posted on Twitter.

"I must say I highly appreciate the enormous efforts and the determination of Ukraine in this process. The people of Ukraine have proven incredible strength and motivation and stamina. So, I am deeply convinced that we will together, you will overcome this atrocious war. We will, and you will, rebuild this beautiful country and modernize Ukraine," von der Leyen said.

Von der Leyen said this is her second visit to Kyiv.

"The brutal fighting continues in the east and in the south. But I must say it is impressive to see how strong the Ukrainians are defending, courageously, their country in this very difficult conditions," Von der Leyen said.

-ABC News' Somayeh Malekian

Ukrainian President Volodymyr Zelenskyy warned of continued devastation on par with what has been seen in Mariupol and Volnovakha amid heavy fighting in the eastern part of the country.

"Russia wants to destroy every city in Donbas, 'every' is not an exaggeration," he said in his latest national address.

"This is probably the fastest example of the complete degradation of any state -- the path that the Russian state has covered in 107 days," the president continued.

In recent days, Russian forces have encircled Severodonetsk, the largest city still held by Ukrainian troops in contested Donbas. Zelenskky has said the battle there could determine the fate of eastern Ukraine.

"The Ukrainian troops are doing everything to stop the offensive of the occupiers. As much as possible. As much as the heavy weapons, modern artillery -- all that we have asked and continue to ask our partners for -- allow them to," the president said Friday.

Up to 100 Ukrainian soldiers are killed and another 500 are injured each day, according to Ukrainian Defense Minister Oleksiy Reznikov.

Reznikov said in a Facebook post Thursday that Russia has "many more means in store to devour human lives in a bid to satisfy its imperial ego."

"That is why we emphasize: Ukraine desperately needs heavy weapons, and very fast," Reznikov said.

Among the weapons he's requesting are "fighter jets, anti-aircraft and missile defence systems to protect our skies."

-ABC News' Will Gretsky

At least 4.8 million Ukrainian refugees are now scattered across 44 countries in Europe, according to the United Nations High Commissioner for Refugees.

The UNHCR has recorded 7.3 million border crossings from Ukraine and another 2.3 million crossings back into the country.

"Although the security situation in Ukraine remains fragile, crossings back and forth have been recorded," the agency said in a statement. "Some cross to Ukraine to assess the situation, check property, visit family members or help them to leave. Others are going to Western Ukraine and areas around Kyiv and Chernihiv intending to stay. Many who have moved back have found their homes severely damaged and struggled to find jobs -- as the war continues to have a devastating economic impact -- and had no choice but to leave again."

-ABC News' Will Gretsky

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