The security forces launched the operations in Sheikh Musri and Siasang localities of Surkhrod district on Tuesday night, Xinhua news agency reported.
A number of arms have also been seized from the possessions of the arrested, the official added.
Without providing more details, the official added that no civilians had been hurt during the operations.
The arrests came after the shooting on a checkpoint by unidentified gunmen in Jalalabad city, the capital of Nangarhar province, on Monday night that left three dead and injured another.
Daesh, or the Islamic State group, which had claimed responsibility for some terrorist attacks over the past couple of months in Nangarhar province, is yet to make comment on the report.
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