The Liberation Tigers of Tamil Eelam (LTTE) said members of their eastern units had taken the children from Vinayagapuram and those responsible had been suspended.
Rasiah Ilanthiriyan, an LTTE military spokesman, said: "It was a mistake by the field commanders, but we are taking strict disciplinary action against our own people involved in this."
The defence ministry accused the Tigers of taking the students and teachers to a military training facility.
The youngsters, who were attending a night tuition class, were taken to an LTTE training camp at Kanjikudichchiaru, the ministry said in a statement.
The statement said: "The devastated parents of the abducted children have made a complaint to the Sri Lanka Monitoring Mission [SLMM] and afterwards left ... in search of their children."
Child soldiers
Norwegian-led monitors said they had no immediate information about the incident while Unicef said they were waiting to hear from field officers in the area where the abduction took place.
LTTE separatists and a breakaway faction - known as the Karuna group - have been accused of conscripting child soldiers.
Nordic truce monitors suspect Karuna is supported by some elements of the military and the UN has accused the military of colluding in their forced recruitment.
The military has denied helping the Karuna group to round up children to be enlisted as fighters.
Sri Lanka has seen a large number of abductions this year, which have been blamed both on the Tigers and Karuna.
Civil war in Sir Lanka started in 1983, with the Tamil Tigers fighting for the independence of the minority Tamil community in the north and east of the country.
The war is estimated to have killed more than 67,000 people and displaced tens of thousands of others.
