Russia’s offensive in eastern Ukraine could be just as dangerous as its failed first offensive north of Kyiv, CIA Director William Burns said Saturday.

Russian President Vladimir Putin is "in a frame of mind that he thinks he cannot afford to lose, so the stakes are quite high in this phase," Burns said during an event in Washington, D.C., hosted by the Financial Times.

Burns said he does not think that Putin has been deterred by the huge amount of Western military support for Ukraine and the resolve of Ukraine’s population and its military.

"I don't think this means that, you know, Putin is deterred at this point, because he staked so much on the choice that he made to launch this invasion that I think he's convinced right now that doubling down still will enable him to make progress," he said.

Burns called Putin's invasion a "profound mistake."

"It was Putin's biggest mistake in planning for this invasion," he said. "And then in launching it, don't underestimate Ukrainians. And I think it's equally a mistake for any of us to underestimate what they bring to the table in intelligence terms in defending their own country."

-ABC News' Luis Martinez

A Russian bomb hit a school in eastern Ukraine where about 90 people had taken shelter, according to a local official.

About 30 people have been rescued so far following the shelling Saturday in the village of Bilohorivka, said Serhiy Haidai, the regional governor of Luhansk.

Two bodies were found under the rubble, Ukraine's emergency services said.

The rescue operation will resume on Sunday.

-ABC News' Jason Volack

All women, children and the elderly have been evacuated from the Azovstal steel plant in Mariupol which has been long besieged by Russian forces, Iryna Vereshchuk, Ukraine's deputy prime minister, said Saturday.

"The president's order has been carried out: all women, children and the elderly have been evacuated from Azovstal. This part of the Mariupol humanitarian operation has been completed," Vereshchuk said in a statement posted on telegram.

Since Thursday, 51 people -- including 11 children -- have been evacuated from the plant, according to Russia's Ministry of Defense.

-ABC News' Jason Volack

First lady Jill Biden met with Ukrainian refugees on Saturday and was briefed on humanitarian efforts from United Nations agencies, nongovernmental organizations and the Romanian government during her trip to Romania.

Biden also visited a Romanian public school, Școala Gimnazială Uruguay, that is hosting Ukrainian refugee students, with Romanian first lady Carmen Iohannis.

Biden spoke with Ukrainian and Romanian educators and met with Ukrainian refugee students and Romanian students in classroom settings.

Biden met with Ukrainian and Romanian children who were making “hands” out of pieces of paper decorated as the Ukrainian and Romanian flags. Some of the children wrote messages on the hands.

Madalina Turza, the senior coordinator of humanitarian assistance for Romania told Biden they are working with the country’s Association of Psychologist to train educators in trauma-informed teaching. She also noted that they are working to make sure that all students are integrated and not segregated from Romanian children, saying that while the refugees may want to stick together at the moment, in time they will need to be with Romanian kids.

Biden also participated in a listening session with Ukrainian educators and mothers.

One mother explained that she escaped Kharkiv with her 8-year-old daughter just two weeks ago and narrowly avoided death when she chose to take one route out of the city over another that was shelled that day. She had been hiding in a basement with her daughter for over a week when they decided to flee.

-ABC News' Allie Pecorin and Armando Garcia

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