According to local government officials, the two students were accused of spying for the central government by Taliban militants.
Deputy provincial police chief Abdul Qadir Khan Omid confirmed that Taliban militants executed two students in Nari district early Saturday.
He said Afghan forces have launched an operation to detain those involved behind the assassination of the two students.
Taliba militants group has not commented regarding the incident so far.
Kunar is among the volatile provinces in eastern Afghanistan where anti-government armed militant groups are actively operating and frequently carry out insurgency activities.