All 400,000 Afghan police and soldiers have been deployed to provide security for voters. Photo: Reuters
People in Afghanistan are voting for a new president in what will be the nation's first ever transfer of power through the ballot box.
Turnout is reported to be brisk despite heavy rain and worries over security.
A massive operation is under way to thwart the Taliban who have vowed to disrupt the election.
Eight candidates are vying to succeed Hamid Karzai, who is barred by the constitution from seeking a third consecutive term as president.
A policeman stands near a billboard for the presidential election at a checkpoint in Kabul, April 4, 2014, before Saturday's presidential election. Photo: Reuters
Heavy rain was falling in Kabul early on Saturday and BBC correspondents said young voters in particular were defying the conditions and the security threats.
Voting has been extended for an hour until 17:00 local time (12:30 GMT).
Many women are taking part in the polls, although not in the same numbers as men.
"I'm not afraid of Taliban threats, we will die one day anyway. I want my vote to be a slap in the face of the Taliban," Kabul housewife Laila Neyazi told AFP.
The biggest military operation since the fall of the Taliban in 2001 has been rolled out for the vote, says the BBC's David Loyn in the Afghan capital. All 400,000 of Afghanistan's police and soldiers were said to be on duty for the election.
Traffic was prevented from entering the Afghan capital from midday on Friday, with police checkpoints erected at every junction.
However, in parts of the capital voters could be seen queuing an hour before polls opened and there is a good-natured, almost carnival atmosphere, with many people on the streets, our correspondent reports.
The BBC's Karen Allen in northern Afghanistan says that large queues also formed there as people waited to cast their ballots. One young voter told our correspondent he had defied his father's warning not to vote because of the threat of violence.
However, some polling stations in the provinces of Herat in the west and Kapisa, north-east of Kabul, were closed because of a combination of the bad weather and security risks.
There have been reports of sporadic attacks at some polling stations, with 10% of stations declared unsafe to open by the election commission.
There were also reports elsewhere of several polling centres not receiving ballot materials in time and of ballot papers running out at some stations.
Fears of fraud, which has marred previous polls in Afghanistan, resurfaced with reports from the southern province of Kandahar that police were preventing voters and observers from reaching polling stations.
Also on Saturday the interior ministry said two police were arrested in Wardak province for stuffing ballot boxes.
Concerns were also raised before the poll about the possible presence of "ghost" polling stations as well as the fact that the number of election cards in circulation appears to be vastly more than the number of registered voters.
However, international observers are optimistic that both the tight security and a number of new guarantees against fraud will make this a fairer election than Afghanistan has seen before, our Kabul correspondent says.
Afghans have been barred from sending text messages until polls close to prevent the service from being used for last-minute campaigning.
There are eight candidates for president, but three are considered frontrunners - former foreign ministers Abdullah Abdullah and Zalmai Rassoul, and former finance minister Ashraf Ghani Ahmadzai.
Dr Abdullah has fought a polished campaign, Mr Ghani has strong support among the new urban youth vote and Dr Rassoul is believed to favoured by Hamid Karzai, our correspondent says.
However, no candidate is expected to secure more than the 50% of the vote needed to be the outright winner, which means there is likely to be a second round run-off on 28 May.
In the latest in a string of deadly attacks that marred the lead-up to the election, award-winning German photographer Anja Niedringhaus was killed and veteran Canadian reporter Kathy Gannon was injured when a police commander opened fire on their car in the eastern town of Khost on Friday.
The run-up to the historic poll has been the bloodiest since the fall of the Taliban, says the BBC's Lyse Doucet.
The heavily-guarded interior ministry, the main compound of the Independent Election Commission and the popular five-star Serena Hotel have all been attacked.