Chaudhry said the inquiry will be conducted by a brigadier and two lieutenant colonels.
"Those involved in this incident will be given the severest punishment possible," said Chaudhry.
"Rangers have not been given authority to shoot and kill a citizen in this manner, so as soon as our findings from inquiry are in, we will take the strictest action possible... Rangers are only allowed to fire in self defense."
Chaudhry added that those involved in the killing were immediately arrested and an FIR was registered against them.
PM's warning
Prime Minister Yousuf Raza Gilan told lawmakers on Thursday it was illegal to abuse state institutions, after an MP called the paramilitary "terrorists in uniform" over the killing of an unarmed man in Karachi.
Gilani warned parliamentarians that under article 63 of the constitution, abusive language could not be used against the superior judiciary and armed forces, according to state news agency APP.
"The PM requested the chair to expunge the language being used against institutions," the agency reported.
Earlier, lawmaker Khwaja Saad Rafique from the opposition Pakistan Muslim League N party, used "foul language" against the Ranger paramilitary force, calling them "terrorists in uniform" who must be "bridled", APP said.
Five members of the paramilitary unit were being held in connection with the killing of a young man at point blank range in a park, which was filmed live and broadcast on television.
President asks for inquiry report
President Asif Ali Zardari summoned a report of the Karachi incident of rangers killing. PM ordered an inquiry into the matter. He promised to personally handle the incident.
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