The group has also named one of its sub-divisions after slain cleric Abdul Rasheed Ghazi, who was killed in the 2007 military operation, the report said.
Ansar al-Islam released a video that starts with a "slickly edited" training montage showing fighters of the Ansar al-Islam engaged in various exercises and posing for the camera, their faces covered.
Then, in a departure from the norm, the video segues into a tribute to Ghazi, Dawn daily reported.
Former military ruler Pervez Musharraf, who had ordered the operation, is currently facing trial for the killing of the cleric.
Ansar al-Islam operates in the Kurdish-dominated northern Iraq and aims at setting up an Islamist state.