Air force jets hit a "Senchcholai", an orphanage run by the Liberation Tigers of Tamil Eelam (LTTE), in the northeastern region of Mullaitivu, the Tigers said in a statement.
The government denied the attack and said the air force had only targeted an LTTE training facility in Mullaitivu.
The Tigers said the victims were students aged between 15 and 18 who were taking part in a two-day seminar on first aid.
"The number of children killed in the Sri Lankan air force bombing on students participating in a first aid seminar has increased to 61, with many fearing that the number killed is higher," the LTTE said in a statement.
About 150 children were seriously wounded, it said, adding that the victims were being taken to hospitals in Kilinochchi and Mullaitivu, both in rebel-held territory in the north.
The LTTE's website showed pictures of some of the children killed in the attack.
"It is a lie to say that schoolchildren were targeted," government spokesman Chandrapala Liyanag