The strikes were launched late Monday after Operations Command of the Afghan National Army Special Operations Corps (ANASOC) approved the sorties to be conducted on militants' positions in Alishing and neighboring Alingar districts, ANASOC said in a statement.
"The army's special forces will spare no effort to intensify attacks against the militants' key figures to eliminate them and kick them out of battle," the statement read.
The sorties also led to the destruction of some of the structures in the target area.
Taliban militants are active in parts of the Laghman, 90 km east of the country's capital Kabul.
Fighting rages across Afghanistan as Taliban militants have been attempting to take territory and consolidate their positions ahead of the winter in the mountainous country.
The Taliban militant group has not made comments yet.