A suicide bomber targeted the sports hall of the base, sources told Al Jazeera.
In a separate attack, responsibility for which was claimed by the Taliban, three Canadian soldiers were killed in Kandahar province, our correspondent said.
'Stop killing us'
In Jalalabad, capital of Nangarhar province, which borders Kunar, around 200 university students rallied in the streets on Wednesday, demanding those responsible for the alleged weekend attack be brought to justice.
In Kabul, the Afghan capital, a crowd of around a hundred, mostly young men, gathered in a western district to vent their frustration at the killings.
"Obama! Obama! Take your soldiers out of Afghanistan!" the protesters chanted, wearing blue headbands with the words: "Stop killing us!"
Others held placards with pictures of young dead children they said were killed by foreign troops.
International forces in Afghanistan have strenuously denied the Karzai government's accusations.
"The evidence we have is that there were no civilian casualties," a senior officer in Nato's International Security Assistance Force (Isaf) said.
"All the people who are claimed to be dead were all fighting-age males."
The international units involved in the incident were with US special forces, he said, and did not involve Nato troops.
US Colonel Wayne Shanks, an Isaf spokesman, said the incident was under investigation and that the military operation involved had been a "joint operation" between Afghan and foreign forces.
International forces have been in Afghanistan since a 2001 invasion by the US to remove the Taliban from power.
Civilian deaths due to operations conducted by Western forces have enraged ordinary Afghans and made them hugely unpopular.
Although UN figures show far more civilians are killed by the Taliban, deaths at the hands of foreigners spark wide resentment and undermine international forces' attempts to weaken the Taliban by building trust among the peaceful population.