In the past two years, Ghawari said there were at least 13 attacks on the Shiite community in Kabul alone.
The bomber targeted a private building in the Shiite neighborhood of Dasht-i Barcha where a group of young men and women, all high school graduates, were studying for university entrance exams.
No one has claimed responsibility for the attack, although Islamic State (formerly ISIS) has previously said it was responsible for attacks on Shi'ite targets.
At least 100 security forces were killed in the fight for Ghazni, officials have said, with unconfirmed fears that at least as many civilians died.
Mohammad Safdar Mohseni, the head of the provincial council in the northern Baghlan province, said the insurgents set fire to the checkpoints after the attack late on Tuesday in the Baghlan-I Markazi district.
"We can confirm the attack was caused by a suicide bomber on foot".
Mujahid, the Taliban spokesman, denied the insurgents had been routed from Ghazni and said sporadic gun battles were still ongoing.
With parliamentary elections due on October 20, the government had been bracing for more attacks in Kabul and other cities, even while hopes of peace talks with the Taliban had been fuelled by a three day truce during the Eid al-Fitr holiday in June.
The Kabul bombing also followed a fierce five-day Taliban siege on the large eastern city of Ghazni that killed at least 120 security forces and civilians before the insurgents retreated under pressure from Afghan forces backed by USA aerial assaults.
The International Committee of the Red Cross said it was providing dressing packages and oral and intravenous medicine to treat wounded at the provincial hospital.
Afghan forces are conducting clearing operations in the city, but hundreds of civilians have fled, trying to escape the fierce fighting, The Associated Press reported Tuesday.
Taliban also attacked a police checkpoint in the southern Zabul province early on Wednesday, killing four police, according to the provincial police chief, Mustafa Mayar, who said another three officers were wounded. He said seven attackers were killed and five were wounded during the battle, in which the Taliban used artillery and heavy weapons.
U.S. Special Forces and 1st Security Force Assistance Brigade advisers are providing advice to Afghan forces on how to effectively conduct clearance operations and combined-arms integration, he added. The assault on Ghazni was widely seen as a show of force ahead of possible peace talks with the USA, which has been at war in Afghanistan for almost 17 years.
Sarhadi Zwak, spokesman for the governor of the eastern Laghman province, says the victims were girls, aged 10-12, who were gathering firewood on Wednesday.
"The extreme human suffering caused by the fighting in Ghazni highlights the urgent need for the war in Afghanistan to end", the top United Nations official in Afghanistan, Tadamichi Yamamoto, said in a statement.