HuJI spokesperson Abu Hanzala issued a statement in which it said it would take revenge from the US for Kashmiri's death, Dawn news and other channels reported.
The channels said they had received a fax message from HuJI confirming the 47-year-old Kashmiri's death. The al-Qaeda-linked terrorist was a key suspect in the 2008 Mumbai terror attacks.
BBC Urdu had earlier reported that Kashmiri was among nine militants killed in a US drone strike in the South Waziristan tribal region.
The US drones targeted a location 20 km from Wana, one of the main towns in South Waziristan late last night.
A drone fired two missiles at the spot and two more missiles were fired after a short interval, local residents were quoted as saying by BBC Urdu.