Kumar's father Lt Col (retd) Karamveer Singh submitted that the murder FIR in the case was illegal.
The top court's directive means Major Aditya Kumar can neither be called for interrogation nor be arrested by the police.
The petitioner also sought directions to issue guidelines to protect the rights of soldiers and for adequate compensation, so that no Army personnel is harassed by the initiation of criminal proceedings for bonafide action in the exercise of their duties.
Meanwhile, the Jammu and Kashmir Coalition of Civil Society (JKCCS), a Kashmir based human rights group in, has termed the SCI's order staying the police investigation against Major Aditya Kumar of 10 Garhwal Rifles as "irregular and against the established norms of criminal procedure" and "appears to favor the accused, at the cost of the victims".
Two youths were killed on the spot, while the third one succumbed to his injuries later at the hospital.
Former army chief V.P. Malik on Sunday demanded withdrawal of an FIR registered by Jammu and Kashmir police against an army officer in connection with the recent firing in Shopian. Later Chief minister, Mehbooba Mufti ordered an inquiry into the incident.
Singh also said that his son's intention was to save army personnel and property and the fire was inflicted "only to impair and provide a safe escape from a savage and violent mob engaged in terrorist activity".
The Supreme Court on Monday put a stay on the FIR against Major Aditya in Shopian firing case and issued a notice to the Centre and J&K govt.
Kashmir, a disputed territory over which India and Pakistan have fought three major wars in the past 70 years, has been of late witnessing a surge in militant attacks and stone-pelting by civilians on Indian security forces. The complainants said they were disturbed by the assaults by unruly and disruptive mob on security forces.