Serhiy Hayday, head of the Luhansk regional military administration, said the school building was destroyed.
"The explosion happened inside the building. Rescuers (are) dismantling the debris as quickly as possible. The chances of finding (anyone still) alive are very small. There were 90 people inside the school building; 27 survived, 60 people most likely died," Hayday said.
Hayday said a Russian air strike hit the school in the village of Bilohorivka, which is some seven miles from the front lines of the ongoing conflict in eastern Ukraine, at around 4:37 p.m. (9:37 a.m. ET) on Saturday, causing fires to break out that took almost four hours to extinguish.
Photos shared from the scene showed rescue personnel searching the smoldering ruins of the school building.
Survivors of the bombing described their harrowing experience in interviews with CNN.
"I got slammed down by a slab -- bent into a ball," said a man with a bandage across his nose and forehead, who preferred not to give his name out of privacy concerns. "Then another explosion, small rocks fell on us. Darkness."
He continued: "There was a woman in our room screaming the whole time. She was pulled out and screaming the whole time. I told her, 'Don't scream.' We couldn't hear a thing."
"They started digging," he said. "I got out. I was like a drunk man -- lost."
Video of the school shared by Hayday on Telegram shows a building that was completely leveled by the attack.
Another survivor, Sergiy, said that he was in the school's basement when the bomb hit and that all three floors of the building collapsed "to the ground."
"We didn't understand anything," Sergiy said. "We were inside. All at once, everything fell down. Darkness. That's it."
Yevgen, meanwhile, described a desperate escape.
"I was the very first one to start climbing out," he said. "I was raking bricks and throwing them out. There were wooden planks and boards. Locals who weren't in the basement helped and used a pipe to rip those boards off."
The survivors said that among the neighbors they were sheltering with were several elderly grandparents.
"Imagine what they bombed," said Sergiy. "An ordinary village with only pensioners and children."
United Nations Crisis Coordinator for Ukraine and UN Assistant Secretary-General Amin Awad in a statement Sunday called the bombing "yet another stark reminder of the cruelty of this war."
"Civilians and civilian infrastructure must be spared in times of war; these obligations under international humanitarian law are non-negotiable," Awad said. "The sooner we seek a peaceful end to the war, the better for the people here in Ukraine and everywhere in the world."
Western countries reacted to the bombing with outrage. UK Foreign Secretary Liz Truss said on Sunday that she was "horrified," adding: "Deliberate targeting of civilians & civilian infrastructure amounts to war crimes. We will ensure Putin's regime is held accountable."
Russian forces have struck fleeing or sheltering civilians on numerous occasions since Moscow invaded Ukraine.
Schools, nurseries and hospitals have all been targeted by Russia, according to the United Nations.
Amnesty International said Friday that Russian forces "must face justice for a series of war crimes" committed in the region northwest of Kyiv, following an investigation the group conducted in Ukraine.
The investigation, based "on dozens of interviews and extensive review of material evidence," has documented "unlawful air strikes on Borodyanka, and extrajudicial executions in other towns and villages including Bucha, Andriivka, Zdvyzhivka and Vorzel."
Fighting in Luhansk has been raging for months, and particularly since Russia refocused its invasion on the eastern Donbas region.
Hayday said on Ukrainian television on Saturday, hours before the school bombing, that the situation was difficult.
"The biggest efforts made by the enemy are to break through in Popasna and the direction of Severodonetsk and Voievodivka. That's where they deployed the biggest amount of their troops and equipment," he said.
"That's where the largest number of shellings and rockets, and air strikes are constant -- it's just a terrible situation. Our guys are holding on, we are waiting for help, for reinforcement," he said.
This story has been updated with additional information.