Commander Safiullah was involved in planning and execution of improvised explosive device attacks on security forces, extortion and kidnapping for ransom, army said.
The Frontier Corps South soldiers were attacked in the mountainous Buleda area of Kech district on Friday.
While chairing the 243rd Corps Commanders' Conference at the General Headquarters in Rawalpindi, Gen Bajwa reiterated Pakistan's firm commitment to peace.
The post of Chief of General Staff (CGS) is considered the most influential position within the army after that of the army chief.
The Taliban seized power in Afghanistan on August 15, two weeks before the US was set to complete its troop withdrawal after a costly two-decade war.
No one immediately claimed responsibility for the attack, but Baloch separatist groups have often claimed such attacks in the recent past.
The meeting took place a day after PM Imran Khan criticised the US for seeing Pakistan's utility only for clearing the mess in Afghanistan.
US Defence Secretary Lloyd Austin expressed his interest in continuing to improve the US-Pakistan relationship and build upon their multiple shared interests in the region.
Pakistan started the fence along the 2,611-kilometer border with Afghanistan — known as the Durand Line — in 2017 when militants repeatedly launched cross-border attacks on Pakistani posts.
The Pakistan Army has been repairing and building its military infrastructure in border areas, even though peace prevails following the ceasefire agreement.
In a statement, the army said that security forces conducted an operation in Zewa, Kurram district on reported presence of three terrorists.
The sources said the IED used in the June 27 attack on the IAF station "definitely" used the technical expertise of the Pakistani military.
The VT-4 is compatible with any modern tank in the world integrating advanced armour protection, maneuverability, fire power capabilities and state-of-the-art technology.
Four soldiers including a junior commissioned officer of FC Balochistan were killed, according to a statement by the army.
The Line of Control between India and Pakistan saw a pleasant change on Thursday with the soldiers of both India and Pakistan exchanging sweets and pleasantries on the occasion of Eid.