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

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