The interior ministry started registering candidates from 8:00 am (0330 GMT), 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.
Under the constitution, Ahmadinejad cannot stand for a third consecutive term.
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.
Among them are heavyweights Ali Akbar Velayati -- foreign minister from 1981 to 1997 and current foreign affairs adviser to Khamenei -- and Mohammad Baqer Qalibaf, a former national police chief who is now mayor of Tehran.
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.
Those calls echo similar ones to Khatami's moderate conservative predecessor, Akbar Hashemi Rafsanjani.
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.
Hundreds of thousands of people poured onto the streets after Ahmadinejad's re-election, when reformist candidates Mir Hossein Mousavi and Mehdi Karroubi cried foul over suspected widespread fraud.
The protests provoked a heavy-handed crackdown by the authorities.
Reformists have been driven into the shadows since then, with Mousavi and Karroubi both put under house arrest more than two years ago.
The vetting process by the Guardians Council is based on articles of the constitution, which calls for candidates to have a political and religious background, and to believe in the principles of the Islamic republic and its official religion.
Any hopeful must be at least 18 years old, but an upper age limit has not been specified.
The candidates who pass the council's screening will have three weeks to campaign ahead of the elections.
In 2009, a total of 475 Iranians registered as prospective candidates but only four were cleared to run, including Mohsen Rezaei, a former commander of the Revolutionary Guards, who is expected to stand again.
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