The decision to reopen the mosques was made in consultation with the ministry of health, IRIB quoted Mohammad Qomi, the director of the Islamic Development Organization, as saying.
Qomi said later on Monday that mosques would only be open for three days commemorating specific nights for the holy month of Ramadan and it was unclear whether they would stay open, according to the Fars news agency.
The move comes even though some parts of the country have seen a rise in infections.
Tasnim news agency reported on Sunday that a county in southwestern Iran had been placed under lockdown. It also quoted the governor of Khuzestan province, where the county is located, as saying there had been a sharp rise in new cases across the province.
Last Friday, prayer gatherings resumed in up to 180 Iranian cities and towns seen as being at low risk of coronavirus contagion after a two-month suspension, state media reported.
The resumption of Friday prayers — still banned in the capital Tehran and some other major cities — followed the reopening last Monday of 132 mosques in areas consistently free of the virus.
Schools will reopen next week, President Hassan Rouhani said on Sunday, according to the official presidency website.
Iran has already lifted a ban on inter-city trips and malls, with large shopping centers resuming activities.
Iran's coronavirus deaths rose by 45 in the past 24 hours to 6,685, Health Ministry spokesman Kianush Jahanpur said in a statement on state TV. It has 109,286 diagnosed cases.
Iran, one of the countries in the Middle East hit hardest by the novel coronavirus, has begun easing restrictions on normal life in order to support its economy, already battered by U.S. sanctions. Health officials have repeatedly warned, however, that easing restrictions could lead to a renewed spike in the number of infections.
Rouhani also announced the replacement of the minister of industry, mines and trade on Monday, according to the official presidency website, a decision that appeared to be an attempt to boost the economy.
Hossein Modares Khiabani will replace Reza Rahmani as the caretaker head of the ministry, the announcement said without noting why Rahmani was dismissed.
Rouhani called on Khiabani to stabilize car prices, eliminate obstacles for domestic production and expand non-oil exports.
In a letter addressed to Rouhani, Rahmani wrote that the reason for his removal was that the parliament had not agreed to the formation of a ministry of commerce, according to Fars news, which published a copy of the letter.
Rouhani's chief of staff had warned Rahmani that if he did not lobby parliamentarians for the formation of the ministry he would be dismissed, Rahmani wrote.