The rights group said it was concerned about the arrests of human rights defender Mohammad Ali Dadkhah, who is serving a nine-year prison term for belonging to a group accused of plotting to overthrow the government.
Last week, presidential adviser Ali Akbar Javanfekr, director of the state-run Islamic Republic News Agency, was arrested for publishing comments viewed as controversial by the country's ruling clerics.
"We urge the government of Iran to promptly release all those who have been arrested for peacefully exercising their fundamental rights," a statement from the rights council read.
Iranian voters next year pick their successor to Iranian President Mahmoud Ahmadinejad. He secured a second term in office following controversial elections in 2009.
Faezeh Hashemi and Mehdi Hashemi Rafsanjani, the daughter and son of former Iranian President Akbar Hashemi Rafsanjani, were arrested recently for making propaganda against the state.
Former President Akbar Hashemi Rafsanjani was criticized by the conservative leadership for backing opposition leader and former Prime Minister Mir Hossein Mousavi during the 2009 contest.