Criticising law enforcement agencies for "refusing" to draw lessons from previous such experiences, the CPI(M) warned "each death" is bound to further inflame the situation and sought an "immediate end" to the recklessness in the region.
The Left party also insisted that a "credible" probe be initiated into the episode, in which three persons were killed in firing by security forces on Tuesday and said "unarmed" stone-pelting crowd should not be shot at.
"The Centre and state government should issue strict instructions to security forces not to resort to firing and deal with the situation with more calm and peaceful manner," party legislator Mohammed Yusuf Tarigami said.
Hitting out at the agencies further, Tarigami said that "unfortunately" no distinction is being made by police while tackling protesters and militants.
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"Every death is bound to further inflame the situation," he added.
In its statement issued earlier in the day, CPI(M) Politburo demanded a "credible" probe into the circumstances which led to the firing after alleged molestation of a girl by an army personnel on April 12 and said that those responsible for the deaths be arrested "forthwith".
Kashmir, particularly Handwara town in Kupwara district, is tense over the last four days in the wake of the death of three youth and a woman in firing by security personnel during a violent protest against alleged molestation incident.
Curfew-like restrictions continued for the third day in parts of Kashmir and mobile internet services remained affected across the Valley.