Afghanistan President Ashraf Ghani has ordered authorities to investigate 28 December's serial blasts that claimed 40 lives.
The Afghan Presidential Palace in a statement on Twitter said, "Terrorist groups and their backers must know that the Afghan people are united and stand firm to any plot carried out by their enemies; these heinous attacks will not break the resolve of the Afghan people."
"The Afghan government reiterates that it is firmly committed to dismantle and eliminate terrorism; the Afghan Security Forces are on the front lines to safeguard their country and people," the statement added.
The suicide bomber detonated his explosives at the gate of the Tebyan center in the PD6 area of Kabul.
The death toll is expected to rise as some of those injured are critical.
The Taliban has denied any role in the attack.
Meanwhile, the United Nations Assistance Mission in Afghanistan (UNAMA) has condemned the attack.
"UNAMA condemns today's attack on civilians in #Kabul. Preliminary reports indicate high civilian casualty numbers. The Mission's human rights workers on ground establishing facts," the UNAMA tweeted.
UNAMA condemns today’s attack on civilians in #Kabul. Preliminary reports indicate high civilian casualty numbers. The Mission's human rights workers on ground establishing facts. pic.twitter.com/hTnhj46Jw7— UNAMA News (@UNAMAnews) December 28, 2017
Women, children and journalists were among the dead.