Two children and tribal leader killed in separate incidents involving foreign troops.
The US military, however, insists that great precaution is taken during the operations to prevent civilian deaths.
The UN chief’s call essentially echoed what Karzai has been calling for years.
Karzai has frequently voiced his own anger over the deaths of civilians at the hands of foreign troops.
The UN chief was scheduled to meet members of the Afghan parliament and Nato military leaders during his visit.
Ban has not visited Afghanistan since 2007. His visit coincides with a renewed focus on the country by Washington.
Barack Obama, the new US president, has said he may send up to 30,000 additional soldiers to Afghanistan to defeat a resurgent Taliban.
The Taliban, driven out of Kabul in December 2001, has been gaining ground in recent months. The group is blamed for an upsurge in attacks on foreign and Afghan forces.