Ukrainian Prime Minister Volodymyr Groysman expressed condolences and vowed those responsible would face tough punishment.
"It is a great tragedy when children die," he said in televised remarks.
The fire broke out late Friday in the camp's wooden two-storey building where children slept in the resort city of Odessa some 440 kilometres south of the Ukrainian capital Kiev, emergencies services said.
After the blaze was put out three girls aged between 8 and 12 were unaccounted for and later "fragments of two burned children's bodies were found" during work to clear the debris, a services statement said. The services added the search for a missing child was under way with two more hospitalised.
"There is a glimmer of hope that she got scared and ran away and is in shock now," said regional police spokesman Ruslan Forostyak, who said the fire alarm did not sound.
Police said they had opened a criminal case into the blaze whose cause was not immediately known.
"I am lacking words because of outrage and regret," regional governor Maksym Stepanov said on Facebook.
Deadly fires are common in Ukraine and other post-Soviet countries due to outdated infrastructure and a lax approach to fire safety.
In May 2016 a fire killed 17 people in a privately-run care home for the elderly outside Kiev, while in 2011 another blaze left 16 people dead in another home in Ukraine's northwest Rivne region.
In neighbouring Russia, two residents of a home for the elderly and people with disabilities died in a fire in the Ivanovo region late Friday night, investigators said. One victim was in his 50s, and the other in his 60s.
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