The NDS said the cell was affiliated to both Haqqani network and to ISIS.
Saleh was targeted early September while on his way to work. As his convoy drove through the city, a roadside IED was detonated.
The vice president survived the attack with only minor injuries but at least 10 civilians who had been in the immediate area were killed.
The Taliban immediately denied responsibility for the attack.
The NDS meanwhile said Saturday, the 10 insurgents had also been responsible for assassinations and assassination attempts on other senior government officials.