The detentions could signal stepped-up crackdowns on opposition figures ahead of June's presidential election to pick a successor to Mahmoud Ahmadinejad.
Monday's report by Kaleme says Zahra and Narges Mousavi were taken into custody after police searched their homes. Iranian officials did not immediately comment, but the two women have campaigned to free their parents.
Mir Hossein Mousavi was the leader of the Green Movement in the 2009 race against Ahmadinejad and spearheaded massive protests over alleged vote rigging after the outcome.
Mousavi, his wife Zahra Rahnavard and another Ahmadinejad challenger, Mahdi Karroubi, have been under house arrest since early 2011.
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