The children lived about 100 metres from the encounter site in Jugtiyal village of Kupwara, about 100 kilometres north of Jammu and Kashmir capital Srinagar, where a joint team of the Rashtriya Rifles, CRPF and the state police had cornered a group of terrorists.
"It is unfortunate that these kids were hit by stray bullets during the encounter," said Javed Geelani, Inspector General of Police Kashmir.
The operation to flush out the terrorists started in the early hours of Wednesday after a tip-off about their presence. It continued till late afternoon when the army's Northern Command announced the three terrorists had been eliminated.
A policeman was also injured in the eight-hour-long encounter. Police said three rifles and other arms and ammunition were later seized.
This is the second encounter over the last week in which a civilian lost his life. A 15-year-old boy was killed in firing at Padgampora village in south Kashmir's Pulwama district last week after a crowd tried to disrupt the operation.
But there has been a spike in the violence in north Kashmir, particularly Kupwara, in the recent past, a development that is being linked to an increase in infiltration attempts from across the Line of Control. According to the Home Ministry in Delhi, infiltration attempts (364) had gone up by three times in 2016 over the previous year's 121.
Improvements in security agencies picking up intelligence inputs about terrorist movements in the state has also led to a steady increase in the number of gun-fights like the one seen in Kupwara on Wednesday. Last year, there were 97 encounters that led to killing of 146 terrorists and arrests of another 76. But security forces paid a heavy price for the successes; 60 security personnel died in these firefights.