"It is very unfortunate that young boys come out when there is an encounter," she said, adding that the administration was trying to make people aware "not to create obstacles when there is an encounter".
Ms Mufti appeared to lay the blame for the continuing violence at the Hurriyat Conference's door, lamenting that the separatist group had shunned the dialogue route that was "an honourable way out for people to come out of this turmoil".
She separatists had last year rejected her talks offer.
The Chief Minister welcomed Union Home Minister Rajnath Singh's statement in parliament that the Centre was ready to talk to all stakeholders. "I hope better sense will prevail now and they will respond positively to the offer made by the home minister and help us to sort it out the problem we are facing day in and out," she told NDTV.
To the parents, she said "I can only appeal to parents that whenever there is an encounter, try and keep your children away from the encounter site". "Because at that time, firing is on from both sides, militants as well as security forces are firing, allowing the children to go these sites is full of danger".
Ms Mufti's renewed advice to parents came amid reports of deaths of three young men in Kashmir's Budgam district. Police said locals threw stones at the security personnel holding the police cordon about a kilometre from the encounter site apparently to distract them from the job at hand. One terrorist was also killed in Tuesday's encounter that ended about eight hours later.
The administration is wary of civilian deaths in encounters triggering a cyclic round of protests witnessed last year when injuries and deaths by pellet guns - considered less-lethal in comparison to standard firearms issued to security personnel - used to control violent mobs had kept the valley on the boil.