Operations in the last two days by International Security Assistance Forces also have resulted in the arrest of a number of insurgents and the seizure of nearly a ton of homemade explosives, Khaama Press reported.
The Taliban leader, who was not identified, was believed to oversee the placement and distribution of explosive devices throughout northern Kandahar province, ISAF said in a statement.
Several suspected insurgents also were arrested and multiple firearms were seized.
The Haqqani leader, who also was not identified, oversaw operations and a number of terrorist cells in eastern Logar province, ISAF said.
Two insurgents were wounded in a gunfight while Afghan and coalition forces were searching for another Taliban leader. Several assault rifles, shotguns, ammunition and gear were seized.
Haqqani leader Sadiq Jan was killed Friday in Paktiya province. ISAF said he was considered responsible for kidnapping locals and coordinating the movements of weapons and bombs in attacks he directed against Afghan and coalition forces.
Also Friday, 1,650 pounds of homemade explosives were found during an operation in Ghazni province.