A statement released by the Mohmand chapter of the banned Tehrik-e-Taliban Pakistan, which earlier claimed the suicide attack that killed Aslam in Karachi, said detained militants were being "brought out of jail and killed".
The government has increased violence against detained militants, it claimed. "We know who they are, we even have their names, addresses, and number of kids (of those) who are torturing our men in custody in Karachi jail," the statement said.
"Therefore, for the sake of your children, stop this practice of torturing and killing Taliban in your custody, otherwise the Lions of Allah will target you any time," it added.
The Taliban further warned jail officials in Karachi against shifting the group's jailed cadres.
Aslam, who led a drive against militants despite several attempts on his life, was killed with two other policemen in the suicide attack on January 9.