Karzai described NATO strikes as "illegitimate," noting the need to protect against civilian casualties means such operations should end, The New York Times reports.
A long series of civilian deaths tied to NATO operations has frustrated Kabul. NATO forces this week put limits on their strike capacity when targeting Taliban militants near civilians.
NATO forces by 2014 are to hand security responsibility over to Afghan forces. Karzai's military has authority over some operations already. The Afghan president said bilateral agreements with NATO further restricted the role of international forces.
"An agreement has been reached clearly with NATO that no bombardment of civilian homes is allowed for any reason," he was quoted as saying.
NATO forces in Afghanistan had said there would be no more aerial attacks on civilian buildings in the country. NATO commander U.S. Gen. John Allen, of the U.S. Marine Corps, however, said airstrikes were permissible in self-defense "if no other options are available."