The interior ministry said another two militants were wounded in the operations while four others were arrested, Khaama Press reported Saturday.
The operations, conducted in Laghman, Kapisa, Zabul, Logar, Ghazni and Paktiya provinces in the previous 24 hours, involved the coordinated forces of the national police, army and intelligence service, the ministry said in a statement.
Weapons, ammunition and explosives were seized during the operation.
Separately, Afghan national police seized six improvised explosive devices in Kunar, Uruzgan and Khost provinces.
In an unrelated operation, a U.S. drone strike killed at least nine members of the Taliban that local Afghan security forces said were attending a meeting in eastern Nuristan province.
Provincial security chief Abdul Baqi Nuristani said at least five of the dead were Pakistani nationals from Punjab province.