Rouhani, a 68-year-old moderate cleric who spearheaded a 2015 nuclear deal with world powers, has sought to frame the election as a choice between greater civil liberties and "extremism".
But he faces stiff competition from hardline cleric Ebrahim Raisi, 56, who has positioned himself as a defender of the poor and called for a much tougher line with the West.
"We are still not pleased with the situation, but in the four years of Rouhani there has been a relative improvement and I'm voting to keep that," said Alireza Nikpour, a 40-year-old photographer in Tehran.
The president and his popular foreign minister Mohammad Javad Zarif were swarmed by supporters as they voted early in the capital.
Together, they helped secure the landmark deal with six powers led by the United States that eased crippling economic sanctions in exchange for curbs to Iran's nuclear programme.
"The enthusiastic participation of Iranians in the election reinforces our national power and security," said Rouhani after casting his vote.
Raisi says he will stick by the nuclear deal, but points to a persistent economic slump as evidence Rouhani's diplomatic efforts have failed.
"Instead of using the capable hands of our young people to resolve problems, they are putting our economy in the hands of foreigners," he said at a closing campaign rally in second city Mashhad on Wednesday.
He has targeted working-class voters hit by high unemployment and subsidy cuts, as well as those who worry the values of the 1979 revolution are under threat.
"I think the most important factors are the ones we had a revolution for, like establishing social justice and removing poverty," said 23-year-old engineering student Mohammad Ali Serkani at a polling station in Tehran.
"I voted Raisi because the Rouhani government and the nuclear deal stopped a lot of research in scientific fields such as nuclear, missile and space technology," he added.
Rouhani has warned that hardliners must be kept away from Iran's diplomatic levers at a delicate moment in relations with the United States.
"One wrong decision by the president can mean war," he said at his own Mashhad rally.
Rouhani gained a reprieve on Wednesday when Washington agreed to continue waiving nuclear-related sanctions, keeping the deal on track for now.
Supreme leader Ayatollah Ali Khamenei cast his vote at his compound in Tehran just minutes after polls opened, saying: "The destiny of the country is in the hands of Iranians."
Long queues formed at polling stations around the country after a short but gripping campaign that has again captivated the nation of 80 million.
"For me, Mr Rouhani's dialogue with the world and moderation in society are very important," said Zahra, a 32-year-old PhD student in food science at another Tehran polling station.
Under Rouhani's predecessor, hardliner Mahmoud Ahmadinejad, "the sanctions really hurt us. It was hard to get lab equipment and very difficult to get visas to study abroad. Now my colleagues can travel to France and the US," she said.
Despite the global implications, it is the economy that has dominated the campaign.
Rouhani has brought inflation down from around 40 percent when he took office in 2013, but prices are still rising by nine percent a year.
Oil sales have rebounded since the nuclear deal took effect in January last year, but growth in the rest of the economy has been limited, leaving unemployment at 12.5 percent overall, and almost 30 percent for young people.
Raisi has promised to triple cash handouts to the poor, hoping to pick up voters that once supported Ahmadinejad.
Having proved too independent for the conservative establishment, Ahmadinejad was dramatically barred from standing by the Guardian Council last month as it disqualified all but six of the 1,636 hopefuls who registered.
The presidential race has since narrowed to a two-horse race as other candidates either pulled out or backed Rouhani or Raisi.
Iranians are also voting for local councils, with reformists hoping to topple the conservatives' narrow majority in the capital.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)
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