Rouhani has arrived at the Interior Ministry where candidates enroll on April 14, Trend correspondent reported.
Ebrahim Raisi, a hard-line cleric close to Supreme Leader Ayatollah Ali Khamenei, also announced plans to run, on a promise to fight poverty and corruption.
Also, Raisi, who is commonly believed to be the main conservative rival of President Rouhani, registered for the presidential race on Friday.
Earlier on Wednesday, Iran's former president Mahmoud Ahmadinejad had registered for the upcoming Iranian presidential election.
Critics of the nuclear deal say that the supposed economic benefits of lifted sanctions have yet to trickle down to average Iranians, and palpable frustration in the streets has created a potential opening for conservative opponents.
"From now on, protecting the deal is one of the most important economic and political issues", he said.
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Influential Shi'ite cleric Ebrahim Raisi, the custodian of a powerful organisation in charge of Iran's holiest shrine, appears to be the leading hardline candidate.
Ahmadinejad was accompanied by his confidant former controversial deputies Hamid Baqaee and Rahim Mashae.
This is in keeping with the strategy that Rouhani had espoused prior to assuming the presidency, as when he boasted that his nuclear negotiations with Western powers had helped to maintain a "calm environment" while Iran quietly increased its nuclear enrichment capabilities.
Incumbent President Hasan Fereidun Rouhani is favored to win re-election, and an Ahmadinejad candidacy would split the hardline vote, giving the advantage to President Rouhani.
In 2013 presidential elections more than 460 candidates submitted registrations, however the Guardian Council approved the candidacy of only 8 applicants, rejecting the candidacy of Former Iranian president Hashemi Rafsanjani. While many delegations have come since the lifting of sanctions, "people are not seeing a huge elevation for Iran in terms of the economy or its place on the global stage", she said. The council normally does not approve dissidents or women for the formal candidate list.