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

White House national security advisor Jake Sullivan hinted Thursday of more sanctions coming against Russia in the "next week or two" aimed at targeting ways Moscow is evading sanctions already imposed.

“Where our focus will be over the course of the coming days is on evasion,” Sullivan said Thursday at the Economic Club of Washington. “As Russia tries to adjust to the fact that it’s under this massive economic pressure, what steps do they take to try to evade our sanctions and how do we crack down on that? And I think we'll have some announcements in the next week or two that identify targets that are trying to facilitate that evasion both inside Russia and beyond."

When Sullivan was asked whether sanctions will automatically be lifted if a negotiated peace deal between Russia and Ukraine is worked out, he appeared cautious with his words, saying, “a lot of that depends on what the shape and scope” of the agreement is.

“A lot of it depends on what the Ukrainians, in consultation with us and the Europeans come to agree to," Sullivan said. "You know, we're not going to do a deal over the head of the Ukrainians where we give a bunch of sanctions relief to Russia. But if some measure of sanctions relief were built in to some credible diplomatic solution led by the Ukrainians, that's something that we would happily discuss."

But Sullivan said Russian oligarchs shouldn't expect to ever get back their yachts and other assets seized under sanctions that have been imposed, saying the ultimate goal is "not to give them back” once the war is over.

“The president is actively looking at how we can deal with the fact that as we seize these assets, our goal is not to give them back. Our goal is to put them to a better use than that," Sullivan said. "But I'll be careful in what I say today because there's an ongoing kind of policy process around how we end up dealing with that question. But, rest assured, that the goal is not just to sit on them for a while."

-ABC News' Justin Gomez