"Woman, children and employees of the (rehabilitation) ministry are among the victims", Najib Danish, spokesman for the interior ministry, said.
According to Inter Services Public Relations, the media wing of the military, General Bajwa visited Kabul on Tuesday and during his visit, he had exclusive one on one meeting with Afghanistan President Ashraf Ghani followed by delegations level discussions.
The explosion took place when employees were leaving their offices early for Ramadan.
Kabul police spokesman Hashmat Stanekzai said a suicide bomber on foot struck outside the Rural Rehabilitation and Development Ministry as employees were leaving work.
Both attacks were claimed by IS.More news: MAN Faces His Greatest Enemies In New E3 2018 Trailer
The Islamic State group claimed responsibility for the latest attack in the Afghan capital, which comes a day before the government's ceasefire with the Taliban is expected to start.
A suicide bomber blew himself up at the entrance to the education department, triggering a fierce battle between gunmen and Afghan security forces, Nangarhar provincial governor spokesman Attaullah Khogyani told AFP.
- Storm before the calm?
The source further added that the attack has left at least 5 policemen dead while more than 10 Taliban insurgents were also killed during the clashes.
The government will continue its operations against other groups, such as IS, during the ceasefire. However, they will retaliate with full force in the event of coming under attack.More news: Paris on lockdown as 'armed man takes hostages'
COAS congratulated Afghanistan authorities on recent peace initiatives especially in respect of the holy month of Ramadan/ Eid and wished that these steps gain more of permanence ultimately leading towards an enduring peace.
Afghan Taliban militants on Saturday announced a surprise three-day ceasefire over the Muslim Eid holiday at the end of this week, their first offer of its kind, days after the government declared an unconditional ceasefire of its own against the Taliban.
Even troops in Ghazni have said they will observe the ceasefire.
If it holds, analysts had expressed cautious optimism that the agreements could help build trust between the government and the Taliban and lay the groundwork for peace talks.
Afghanistan has blamed Pakistan for giving assistance to the Taliban and other insurgent groups.More news: Homeowner's association issued gator warning before attack
The latest violence comes as dozens of protesters march hundreds of kilometres towards Kabul to demand an end to the almost 17-year conflict.