The interior ministry started registering candidates from 0900 IST, according to the media reports.
Interior Minister Mostafa Mohammad Najjar advised hopefuls against waiting until the last day to register, while warning against early campaigning, said the state broadcaster's website.
The polls will be followed closely in the West four years after Mahmoud Ahmadinejad's re-election for a second term sparked a wave of violent protests that were suppressed by the regime with deadly force.
His successor is expected to face an array of challenges, including Iran's worsening economy targeted by international sanctions over Tehran's disputed nuclear programme.
The process of screening candidates is entrusted to the Guardians Council, an unelected body controlled by religious conservatives appointed by supreme leader Ayatollah Ali Khamenei, who has the final say on all key issues.
The council is set to announce the names of those who have been cleared to stand no later than May 23.
Many conservative hopefuls have expressed readiness to run in the election.
Ahmadinejad is widely expected to tap his close and controversial aide Esfandiar Rahim Mashaie to run for office.
But Mashaie, a former chief of staff, has become the bane of ultra-conservatives due to his perceived "deviationist" nationalist and liberal views.
On the other side of the spectrum, marginalised reformists are yet to produce a solid candidate. However, reformist newspapers and figures have stepped up calls for former president Mohammad Khatami to run.
Last week, Intelligence Minister Heydar Moslehi implicitly warned both ex-presidents over their alleged role in the protest movement that followed the disputed 2009 elections.
