Four others have been injured in the battle which started on Sunday after Pakistani border forces moved to build a checkpoint in Nari district of Kunar province, local officials said.
Kunar Governor Abdul Satar Mirzakul said that the clash began at 3:00p.m. on Sunday before it was paused at 7:00a.m.
The clash resumed the next day and is ongoing, he said.
This is not the first time that Afghan and Pakistani forces clash along the colonial-era Durand Line, a line drawn up in 1893 and rejected by Afghanistan.
Sediq Sediqi, a spokesman for Afghan president, called on Pakistan to immediately stop shelling.