Iranians have been urged by Supreme Leader Ayatollah Ali Khamenei to turn out in force to vote for a new president to discredit suggestions by the United States that the election would be unfair.
The ballot is the first presidential poll since a disputed 2009 contest led to months of unrest.
This election is unlikely to bring profound change in Iran's rocky ties with the West, but it might bring a softening of the style adopted by outgoing President Mahmoud Ahmadinejad.
World powers in talks with Iran over its nuclear programme are looking for signs of a change of its negotiating stance.
Iran's Gulf Arab neighbours are wary of Iran's influence in Iraq next door and its backing for President Bashar al-Assad and his Lebanese allies Hezbollah in the Syrian civil war.
The Sunni Arab kingdoms are backing the rebels in Syria.
Voting in the capital Tehran, Mr Khamenei called on Iranians to vote in large numbers and derided Western misgivings about the credibility of the vote.
"I recently heard that someone at the US National Security Council said 'we do not accept this election in Iran'," he said.
"We don't give a damn," he added.
On 24 May, US Secretary of State John Kerry called into question the credibility of the election, criticising the disqualification of candidates and accusing Tehran of disrupting internet access.
Iran's Guardian Council, the state body that vets all candidates, has barred a number of hopefuls from the roster in the ballot.
Among those barred is former president Akbar Hashemi Rafsanjani, who is seen as sympathetic to reform.
Iranians can choose from a slate of six candidates, all of whom were approved to run by the Guardian Council.
"What is important is that everyone takes part," Mr Khamenei said.
"Our dear nation should come (to vote) with excitement and liveliness, and know that the destiny of the country is in their hands and the happiness of the country depends on them."