The arrests in recent days are alleged to have targeted unnamed people who run channels on the popular messaging site Telegram supporting reformists and the moderate government of President Hassan Rouhani.
Two prominent journalists - Ehsan Mazandarani and Morad Saghafi - have also been detained.
Mahmoud Sadeghi, a reformist MP, wrote an open letter to Revolutionary Guards commander Mohammad-Ali Jafari, calling on the organisation to stay out of politics.
Several other MPs have also criticised the arrests in open letters this week.
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Outspoken moderate-conservative MP Ali Motahari threatened to seek the impeachment of the intelligence minister if he did not provide details of the arrests.
The Revolutionary Guards operate their own intelligence wing independently of the government and answerable only to supreme leader Ayatollah Ali Khamenei.
Telegram, which has an estimated 20 million users in Iran, has become the leading site for political and cultural discussions in a country where Facebook and Twitter are banned.
The authorities have tried to control the site, demanding that channels with more than 5,000 followers register with the government.
A reformist newspaper also reported today that Faezeh Hashemi, daughter of revolutionary founder Akbar Hashemi Rafsanjani, had again been sentenced to six months for "spreading falsehoods" after she accused the judiciary of corruption.