During the previous presidential election in June 2013, Rouhani garnered 50.7 percent of a total of over 36 million votes.
Influential Shi'ite cleric Ebrahim Raisi appears to be the leading choice so far.
Ardavan Amir-Aslani, a French-Iranian lawyer who advises European companies setting up in Iran, said he would be surprised if Rouhani does not win re-election despite the economic malaise.
Rouhani also referred to his government's "successful" management of economic issues and said that he was able to curb the inflation, raise the rate of economic growth, stop depression and, to some extent, solve unemployment problem.
The politically moderate cleric faces a tougher than expected battle for a second term on May 19 as criticism mounts over the continued stagnation of the economy. Ahmadinejad previously served two four-year terms from 2005 to 2013 pushing forward Iran's nuclear program despite global opposition.
Under the law on presidential elections, a candidate must be Iranian by birth and citizenship, a respected religious and political figure, a competent, virtuous individual committed to the principles of Islamic revolution and the official religion (Shiite Islam), in addition, this person must have solid reputation. Registration for the election begins on Tuesday and will continue until Saturday.
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Ultimate authority rests with Supreme Leader Ayatollah Ali Khamenei, who has accused the West of using women as a tool to advertise products and satisfy "disorderly and unlawful sexual needs".
Ahmadinejad previously said he wasn't going to run after Khamenei advised him not to, saying he would instead support his former deputy Hamid Baghaei who also registered on Wednesday.
Rouhani has arrived at the Interior Ministry where candidates enroll, Trend correspondent reported April 14.
The Guardian Council will assess the qualification of the applicants and announce the names of the qualified candidates by April 27.
"I have come to be the candidate for the whole of Iran".