Authorities said search operations concluded late on Saturday and put the death toll in the strike on the teacher training college at 21, many of them young women.
The building's facade was gashed by gaping holes and smashed windows.
Piles of twisted metal and concrete lay outside the building looking onto what was once a courtyard, with wrecked desks and cupboards piled up inside.
A worker in protective gear examined pieces of metal and other debris laid out on a tarpaulin as workers from Russia's Investigative Committee compiled data from the incident on Friday.
Reuters reported from Starobilsk on a media trip organised by the Ministry of Foreign Affairs of the Russian Federation on Saturday.
Ukraine's military denied responsibility for the attack, saying it had struck an elite drone command unit in the area and that its forces complied with international humanitarian law.
Reuters was not able to independently verify what happened.
"Three waves of UAVs (drones) 10-15 minutes apart," Russia's Human Rights Commissioner, Yana Lantrova, told journalists outside the wrecked building as a group of people held up photos of those killed.
"Sixteen UAVs in total. They waited for the children to run out. They fired directly at the children."
The facility in the east of Ukraine's Luhansk region, annexed by Russia several months after the Kremlin's February 2022 invasion of its smaller neighbour, was adorned with official Russian state symbols.
A set of instructions on how to act against "the threat of terrorism" was posted on one wall.
Russian President Vladimir Putin ordered his military to prepare options for retaliation against Ukraine after the attack.
Within a little more than 24 hours, early on Sunday, Russia struck Kyiv and surrounding areas with hundreds of drones and missiles in one of the heaviest bombardments of the city since the start of the war.
The overnight barrage killed four people and was marked by the firing of a Russian Oreshnik hypersonic missile south of Kyiv.
