Asif made the claim when he appeared before a four-judge bench headed by Chief Justice Iftikhar Chaudhry along with the Attorney General and Baloch leaders.
The court had recently directed Sharif, who earlier held the defence portfolio, to appear in person today or face "serious consequences" over slow progress in the case of 35 "missing persons".
To avoid a confrontation with the apex court, Sharif relinquished the defence portfolio and handed it over to Asif yesterday.
Expressing dissatisfaction at progress in the case, the Chief Justice said people had pinned hopes on the PML-N government but the situation has not changed. Citing instances of people being abducted with the help of helicopters, the bench said the Inter-Service Intelligence agency's name keeps coming up in the case.
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The 35 "missing persons" are believed to be in the custody of intelligence agencies. "Missing persons" is a term used for people detained without charge by security and intelligence agencies.
The bench said the Frontier Corps (FC) is responsible for law and order in Balochistan and asked the paramilitary force's chief to appear before it and explain the situation.
Chaudhry said a case would be registered against the head of the FC if he failed to present the missing persons. He questioned whether the premier had watched television coverage of the families of the missing walking in protest from Quetta to Karachi.