Russian President Vladimir Putin said another 15 people were reported missing and accused Ukrainian forces of deliberately hitting the site.
Reuters was not able to verify what happened independently and there was no comment on Friday from Ukraine, which wants to recapture Luhansk, one of four eastern regions that the Kremlin unilaterally claimed as its own in 2022 in what Ukraine denounced as an illegal land grab.
Both sides deny deliberately targeting civilians.
Putin characterised the incident as a terrorist attack, accusing Ukraine of intentionally targeting civilians.
Yana Lantratova, Russia's human rights commissioner, said that 86 teenagers aged 14 to 18 had been asleep inside the hostel belonging to Luhansk Pedagogical University's Starobilsk college when Ukrainian drones attacked it during the night.
Leonid Pasechnik, the top Russian-installed official in Luhansk, said two people had been pulled from the rubble and Maria Lvova-Belova, presidential commissioner for children's rights, said 18 children could still be trapped.
Some children being treated in hospital were reported to be in a serious condition.
Kremlin spokesman Dmitry Peskov called for those responsible to be punished.
"This is a monstrous crime. An attack on an educational institution where children and young people are present," he told reporters.
Russia said the United Nations Security Council would hold an emergency session in New York later on Friday to discuss the incident.
Russia's foreign ministry said the Ukrainian strike had pulverised the top three of the hostel's five floors.
It said there were no military facilities nearby and that Ukraine must have known what it was attacking: "We call on international organisations, national governments and the global community to give an honest assessment ... and to strongly condemn the bloody terrorist attack."
Photographs and video released by the Russian authorities showed rescue workers stretchering one man out of the rubble, severely damaged buildings - one of which appeared to have partially collapsed - and fires still burning.
Ukrainian President Volodymyr Zelenskiy last week promised retribution after laying red roses at the rubble of a Kyiv apartment building where a Russian missile strike had killed 24 people including three children.
