The Taliban Police Chief in Laghman province confirmed that two members of the group have been killed and four others have been injured in a roadside explosion in the Alingar district.
Local sources said that a Taliban commander has too been killed in the explosion.
Earlier on Monday, an explosion had rocked Mehtarlam, the capital city of Laghman province as a result of which around 15 people had been wounded.
No more details about the explosion had been given by the Taliban.
No one has claimed responsibility for the attacks.