The BBC reported two other soldiers with the North Atlantic Treaty Organization force were injured in the same blast in Nuristan province. Their nationalities also were not released. The region is a stronghold of former prime minister and militant leader Gulbuddin Hekmatyar.
The latest explosion comes in the wake of a major engagement Monday in Zabul province in which 55 insurgents reportedly were killed and another 20 wounded, the report said.
Violence has increased sharply in recent months in southern and eastern Afghanistan because of growing resistance from Taliban fighters.
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