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.
Ahead of the May 19 poll, the interior ministry had announced a ban on live television debates, triggering an outcry that prompted a reversal of its decision. Three live debates are now expected to take place.
Rouhani, who is hoping for a second term in office, and conservative rivals Ebrahim Raisi and Tehran mayor Mohammad Bagher Ghalibaf all rejected the ban.
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On Friday, during the first live debate, Ghalibaf hammered Rouhani and his confidant and first vice-president, Eshaq Jahangiri, with both sides trading accusations of "lies" and making "insincere" comments.
Ghalibaf berated Rouhani for failing to make good on a promise "to create four million jobs", saying unemployment was Iran's "biggest problem".
Rouhani riposted by saying: "I never promised to create four million jobs. That's a lie".
Unemployment, which stands at 12.4 percent, the lack of social housing and government aid to the underprivileged were the issues that dominated Friday's debate.
Ghalibaf also accused Rouhani and his government of "bad management" and of "repeatedly saying that the government does not have the means" to solve the Islamic republic's problems.
He also took a poke at Jahangiri, whose candidacy was a surprise entry at the last minute, saying the vice-president threw his hat in the ring only to back up Rouhani and help him in the debates.
According to several reformists, Jahangiri is expected to pull out of the race after the three live television debates in order to support Rouhani.
Jahangiri dismissed the attacks against himself and accused Ghalibaf of running the capital "with the mentality of a military man".
A war veteran, Ghalibaf is a former Revolutionary Guards commander and police chief. This is his third run at the presidency.
The other three candidates - Raisi, a hardline judge and close ally of supreme leader Ayatollah Ali Khamenei, conservative Mostafa Mirsalim and reformist Mostafa Hashemitaba - kept a low profile during the first debate.
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