President Joe Biden warned: "Don't even think about moving onto one single inch of NATO territory," Saturday in an address that just ended.

Biden spoke to an audience of between 750 and 1,000 attendees in Warsaw, Poland, including Polish President Andrzej Duda, members of parliament, local officials, students from local universities and U.S. embassy staff, according to the White House.

This is a developing story. Check the blog for updates.

"Continuous battles" for Mariupol's territory continue daily, the city's deputy mayor, Serhiy Orlov, told ABC News Saturday.

The deputy mayor estimated that 150,000 people remain in the city.

He was unable to give an update on the hundreds of of civilians believed to have been killed in Russian strikes that hit a theater that was being used as a shelter. A sign indicated that children were sheltering inside satellite imagery shows.

"The situation becomes worse, so people still have a lack of everything," he told ABC News in a remote interview.

The mayor added: "The lack of water, electricity, heat and sanitary system, lack of medicine, food. So they're just surviving … it's not a secret that from 50 to 100 airstrikes, the Russian aircraft do each day and the one-third or one-half of all the bombing of airstrikes in Ukraine goes on Mariupol."

-ABC News' Guy Davies

Two missile strikes in Lviv left five people injured on Saturday, according to preliminary data, the governor of Lviv, Maksym Kozytskyi, said in a statement.

The official said there is still a threat of a missile strike and told people to stay in shelters, not to walk down the street or take pictures of anything.

The Governor of Lviv has asked people not to share footage of the blast site, in a statement.

"Everything that can be reported for security reasons, I will report," Kozytskyi said.

The official could not confirm reports that there was an impact on a residential building or other infrastructure facilities.

Home to many refugees passing through on their way out of the country, Lviv has been spared some of the worst shelling seen so far.

-ABC News' Guy Davies

President Joe Biden met with Ukrainian refugees in Warsaw, Poland, on Saturday. When asked by reporters what he thought of Russia's President Vladimir Putin after meeting with refugees, Biden said, "He’s a butcher."

Biden was greeted by Warsaw Mayor Rafal Trzaskowski and Polish Prime Minister Mateusz Morawiecki outside the PGE Narodowy Stadium and he met several volunteers and refugees.

After meeting with refugees, Biden briefly spoke with reporters and said he’s always in awe of the depth and strength of the human spirit of refugees.

"I’ve been to an awful lot of places like this, a lot of refugee camps, in my life, and what I’m always surprised by, is the depth and strength of the human spirit. I mean it sincerely. They’re -- it’s incredible. It’s incredible. See all those little children? Just want to hug, they just want to say thanks. I mean -- I mean, it just makes you so damn proud," Biden said.

"Each one of those children said something to the effect, say a prayer for my dad, or my grandfather or my brother, who’s back there fighting. And I remember what it’s like when you have someone in a war zone. Every morning you get up and you wonder. You just wonder, you pray you don’t get that phone call," Biden said.

-ABC News' Armando Garcia

All Russian troops have left the Ukrainian cities of Kyiv and Chernihiv, withdrawing north toward the borders of Belarus and Russia to consolidate before likely redeploying to the Donbas region in eastern Ukraine, a senior U.S. defense official told reporters Wednesday.

But even with the Russians gone, the territory remains treacherous.

"There are some indications that they left behind mines and things like that, so the Ukrainians are being somewhat careful in some areas north of Kyiv as they begin to clear the ground and clear the territory and re-occupy it," the official said.

While the U.S. hasn't yet seen these troops redeploy elsewhere in Ukraine, it'll likely happen soon, according to the official. Ukrainian forces are preparing for a major fight in Donbas, the official said.

The official also said the Pentagon is "monitoring" an apparent nitric acid explosion in Ukraine's Luhansk region, which Russia blamed on Ukraine.

"We've seen the Russians claim that this was a Ukrainian attack on this. We do not believe that is true," the official said. "We do believe that the Russians are responsible, but exactly what they used when they did it, why they did it, what the damage is, we just don't have that level of detail," the official said.

The official also noted that a small number of Ukrainians currently in the U.S. for "professional military education" were pulled aside for a couple days of training on Switchblade drones, which the U.S. is sending overseas as part of its military aid, according to the official.

"Although it's not a very difficult system to operate, we took advantage of having them in the country to give them some rudimentary training on that," the official said.

-ABC News' Matt Seyler