"After demands by the Iranian nation and the candidates for a review (of the decision), the presidential elections campaign commission decided... That debates may be broadcast live," the ministry said in a statement on official news agency IRNA.
The U-turn came days after the commission, which sets campaigning rules ahead of the May 19 poll, said the debates would not be broadcast live as in previous elections, sparking outrage on social media.
Televised debates are a relatively new feature of Iranian presidential elections and are believed to have influenced the results of votes in 2009 and 2013.
The ban on live debates was seen as an attempt to avoid embarrassing certain candidates by exposing details about their actions in previous roles.
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Ghalibaf lost momentum in a 2013 election bid after his rival Rouhani said the hardline former police chief had proposed allowing student protests in 1999 so security forces could crush them.
In 2009, live debates between conservative incumbent Mahmoud Ahmadinejad and reformist candidates Mehdi Karroubi and Mir Hossein Mousavi turned into heated exchanges of accusations that many said went too far for the regime.
Prior to the reversal, Interior Minister Abdolreza Rahmani-Fazli, a member of the conservative-dominated commission, defended the ban on live debates, saying it would avoid "insults, accusations and (violations of) public ethical codes".
All six candidates are set to take part in the first debate on Friday, the commission's head told news agency ISNA.
The powerful Guardian Council last week blocked Ahmadinejad from standing for another term.
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