The attacks, which targeted civilian and military institutions in the capital, were organized by the terror group Mahaz Fedayan, Khaama Press reported.
The NDS said in a statement intelligence agents seized suicide bomb vests, military uniforms, weapons and a huge amount of explosives. At least four suspected militants were arrested.
Meanwhile, an explosion was heard in Afghanistan's western Herat province Saturday evening, Khaama Press said.
The incident took place near the provincial government building.
Abdul Rauf Ahmadi, spokesman for the provincial security command, confirmed the explosion but said it was unclear what caused the blast.
There were no reports of casualties.