Provincial security chief, Gen. Abdul Habib Syed Khel said the rockets have landed in Shegal and Dangam districts.
Gen. Syed Khel further added that the cross-border shelling left one civilian dead and 14 others injured, while 20 families were forced to leave their homes in Shegal district.
Local officials urged the interior and foreign affairs ministry to take immediate actions in a bid to stop the cross-border shelling.
Cross-border shelling from the other side of Durand Line continues during the past two years with local officials saying that the rockets are fired by Pakistani military.
According to local authorities in Kunar province, there has been a sharp rise in cross-border shelling from the other side of the border as Afghanistan is getting close to the second round of elections.
The officials also added that the cross-border shelling had considerably increased in eastern provinces of Afghanistan during the first round of election.
Pakistani officials have not commented in this regard so far.