Although all six candidates are seen as conservatives, one of them,
cleric Hassan Rouhani, has been reaching out to the reformists in recent
days.
The election will decide a successor to outgoing leader Mahmoud Ahmadinejad.
His eight years in power have been characterised by economic turmoil and Western sanctions against Iran over its controversial nuclear programme.
Ayatollah's call Some 50 million people are eligible to cast their ballots. Polls across Iran opened at 08:00 local time (03:30 GMT) and were due to close at 18:00 (13:30 GMT).
However, the Iranian Interior Minister, Mostafa Mohammad Najjar, announced that voting time will be extended for another two hours.
The BBC's Mohsen Asgari in Tehran says that in some parts of the country more ballot papers have been requested.
Mahmoud Ahmadinejad cast his ballot in Tehran accompanied by Vice-President Mohammad Reza Rahimi and Government Spokesman Gholam Hoseyn Elham, Iran's Fars news agency reported.
The past week brought a surprising change to what otherwise had looked like being a predictable election, the BBC's Richard Galpin reports.
Mr Rouhani has been attracting increasing attention, speaking publicly about the need to re-engage with the West, our correspondent says.
He has also promised to free political prisoners and called for greater reform of the media.
The surge of support for him came after Mohammad Reza Aref, the only reformist candidate in the race, announced on Tuesday that he was withdrawing his candidature on the advice of pro-reform ex-President Mohammad Khatami.
Mr Rouhani now has the endorsement of two ex-presidents, Mr Khatami and Akbar Hashemi Rafsanjani, who was disqualified from the race by the powerful Guardian Council.
However, Mr Rouhani faces a tough challenge from hardline candidates, including top nuclear negotiator Saeed Jalili and Tehran's mayor Mohammad Baqer Qalibaf.
The remaining candidates are conservatives close to Iran's supreme leader, Ayatollah Khamenei.
He has called for a large turnout but not publicly stated his preference for any single candidate.
After casting his vote early, the supreme leader spoke live on state television.
"Inshallah (God willing), the Iranian people will create a new political epic," he said.
If no candidate secures 50.1% or more of the votes to win outright, a second round will be held in a week's time.
Municipal elections also being held on Friday are being hotly contested in many towns and villages because of competition between families and tribes, the BBC's Mohsen Asgari adds.
Friday's presidential election is the first since 2009 when protesters took to the streets in anger at the results which they said had been rigged in favour of Mr Ahmadinejad.
But the disqualification of Mr Rafsanjani in May left supporters of the post-2009 liberal movement divided about whether to bother voting in the election at all.
No foreign observers will be monitoring the poll and there have also been concerns that media coverage in the run-up was unfair.
Many reform newspapers have been shut down, access to the internet and foreign broadcasters restricted, and journalists detained.
On Thursday, the BBC accused the Iranian authorities of putting "unprecedented levels of intimidation" on BBC employees' families.
It said Iran had warned the families of 15 BBC Persian Service staff that they must stop working for the BBC or their lives in London would be endangered.
Tehran has so far made no comment on the allegation.
The election will decide a successor to outgoing leader Mahmoud Ahmadinejad.
His eight years in power have been characterised by economic turmoil and Western sanctions against Iran over its controversial nuclear programme.
Ayatollah's call Some 50 million people are eligible to cast their ballots. Polls across Iran opened at 08:00 local time (03:30 GMT) and were due to close at 18:00 (13:30 GMT).
However, the Iranian Interior Minister, Mostafa Mohammad Najjar, announced that voting time will be extended for another two hours.
The BBC's Mohsen Asgari in Tehran says that in some parts of the country more ballot papers have been requested.
Continue reading the main story
On the back of a motorbike I head out for a tour of polling
stations in various parts of Tehran. My plan is to go from the north of
the city where I work to the southern part where more working-class
people live. The 18km (11 mile) tree-lined Vali-e-Asr Street connecting
two ends of the city is my best option.
Schools and mosques are polling stations for the day. At most of those I pass there are queues, a mixture of old and young, men and women. As I approach southern parts of Tehran, the lines of people are longer and in some places it is unbelievably crowded.
I found Ebrahim Yazdi, a former foreign minister and now a prominent dissident, in one long queue. "I vote because I love Iran and I am faithful to the process of democracy," he said.
Supreme Leader Ayatollah Khamenei, in his latest remarks, asked all Iranians to vote - even those who did not like the Islamic system.
In one polling station close to Vanak Square, there is a heated debate going on between a group of young people and an old man. He intended to vote for Saeed Jalili. The young men and women were passionately trying to persuade him to vote for Hassan Rouhani.
On-the-scene
Schools and mosques are polling stations for the day. At most of those I pass there are queues, a mixture of old and young, men and women. As I approach southern parts of Tehran, the lines of people are longer and in some places it is unbelievably crowded.
I found Ebrahim Yazdi, a former foreign minister and now a prominent dissident, in one long queue. "I vote because I love Iran and I am faithful to the process of democracy," he said.
Supreme Leader Ayatollah Khamenei, in his latest remarks, asked all Iranians to vote - even those who did not like the Islamic system.
In one polling station close to Vanak Square, there is a heated debate going on between a group of young people and an old man. He intended to vote for Saeed Jalili. The young men and women were passionately trying to persuade him to vote for Hassan Rouhani.
Ballot counting is still expected
to start at midnight local time and results are due to be announced in
the following 24 hours.
The minister also told state TV that presidential candidates
would have three days to lodge complaints to the vetting body, the
Guardian Council, if they were unhappy with the results. Mahmoud Ahmadinejad cast his ballot in Tehran accompanied by Vice-President Mohammad Reza Rahimi and Government Spokesman Gholam Hoseyn Elham, Iran's Fars news agency reported.
The past week brought a surprising change to what otherwise had looked like being a predictable election, the BBC's Richard Galpin reports.
Mr Rouhani has been attracting increasing attention, speaking publicly about the need to re-engage with the West, our correspondent says.
He has also promised to free political prisoners and called for greater reform of the media.
The surge of support for him came after Mohammad Reza Aref, the only reformist candidate in the race, announced on Tuesday that he was withdrawing his candidature on the advice of pro-reform ex-President Mohammad Khatami.
Mr Rouhani now has the endorsement of two ex-presidents, Mr Khatami and Akbar Hashemi Rafsanjani, who was disqualified from the race by the powerful Guardian Council.
However, Mr Rouhani faces a tough challenge from hardline candidates, including top nuclear negotiator Saeed Jalili and Tehran's mayor Mohammad Baqer Qalibaf.
The remaining candidates are conservatives close to Iran's supreme leader, Ayatollah Khamenei.
He has called for a large turnout but not publicly stated his preference for any single candidate.
After casting his vote early, the supreme leader spoke live on state television.
"Inshallah (God willing), the Iranian people will create a new political epic," he said.
Continue reading the main story
Iranian presidential elections
- Six candidates running
- Race is seen as contest between Ayatollah Ali Khamenei loyalists and moderate reformers
- About 50 million eligible voters
- If no candidate wins 50.1%, run-off held on 21 June
He also attacked US criticism of the presidential poll and those, in the US, who said they did not recognise the election.
"The Iranian people... will do what is in their interest."If no candidate secures 50.1% or more of the votes to win outright, a second round will be held in a week's time.
Municipal elections also being held on Friday are being hotly contested in many towns and villages because of competition between families and tribes, the BBC's Mohsen Asgari adds.
Friday's presidential election is the first since 2009 when protesters took to the streets in anger at the results which they said had been rigged in favour of Mr Ahmadinejad.
But the disqualification of Mr Rafsanjani in May left supporters of the post-2009 liberal movement divided about whether to bother voting in the election at all.
No foreign observers will be monitoring the poll and there have also been concerns that media coverage in the run-up was unfair.
Many reform newspapers have been shut down, access to the internet and foreign broadcasters restricted, and journalists detained.
On Thursday, the BBC accused the Iranian authorities of putting "unprecedented levels of intimidation" on BBC employees' families.
It said Iran had warned the families of 15 BBC Persian Service staff that they must stop working for the BBC or their lives in London would be endangered.
Tehran has so far made no comment on the allegation.
