A soldier stands guard near the site of a suicide attack in Kabul. Officials said the attacker was on foot.
One policeman and six civilians were killed and 15 civilians wounded when the bomber was stopped at a security checkpoint in the Mosalla-e Mazar area of Kabul, said Najib Danesh, an interior ministry spokesman.
As per an account of the security officials, over two dozen militants were being trained in the camp as suicide bombers when it came under attack from the CIA-operated pilotless aircraft.
Afghan officials gave a wide range of figures for the number of casualties: a security source told AFP 13 people were killed and more than 30 wounded.
President Mohammad Ashraf Ghani called the attack a crime against humanity.
The State Department has offered a $5 million reward for information on Pakistani Taliban leader Mullah Fazlullah in the latest USA effort to pressure militants in the South Asian nation.
In another incident, seven people were killed when a suicide bomber blew himself up in Kabul.
The death toll has risen to nine, Waheed Majroh, spokesman for the Health Ministry said.
The Taliban also ambushed members of the local police who were sent to assist the soldiers, killing 10 policemen and wounding nine, provincial police spokesman Khali Aseir said.
The spokesman for the Pakistani Taliban says the son of their chief, Mullah Fazlullah, was among 21 "holy warriors" killed this week when missiles fired by a USA drone struck a seminary in Afghanistan.
The development comes as the Taliban face growing pressure to take up the Afghan government's recent offer of peace talks to end a more than 16-year insurgency that has claimed thousands of lives.
Information for this article was contributed by Maamoun Youssef and Kathy Gannon of The Associated Press.