At least 530 people were killed and thousands injured in the quake.
US President Donald Trump has refused to formally certify Iran’s compliance with the nuclear deal. Under that deal, most sanctions on Iran were lifted in exchange for Tehran curbing its nuclear work.
Rouhani is trying to hold on to office by seeking support from reformist voters who are disillusioned by the economy and the slow pace of social reforms.
Although a long shot, the charismatic mayor could emerge as a strong contender to President Rouhani if he manages to beat the other hardliners.
Rouhani responded to the challenges posed over the nuclear deal payoff by saying oil prices have surged and the economy just needed more time to recover.
Rouhani has already won the backing of former president Mohammad Khatami, considered the spiritual leader of the reformists, who declared his support on his website on May 2.
Hardliners attacked pragmatist Rouhani’s economic record and said that the Islamic Republic would be harmed if he was re-elected.
He said that Iran’s economy had improved since his election but his views clash with Khamenei and other hardliners who dislike his policy towards the West.
The Guardian Council approved six candidates but disqualified former President Mahmoud Ahmadinejad, who had been warned by Khamenei not to enter the race.
Prominent conservatives have, however thrown their weight behind Rouhani, who has a policy of open-mindedness towards the West, which would benefit Iran.