A massive security operation is under way to thwart the Taliban which has 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.
The poll has already been overshadowed by the shooting of two journalists.
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. They had both worked for Associated Press for many years.
It was the latest in a string of deadly attacks that marred the lead-up to the election.
The biggest military operation since the fall of the Taliban in 2001 has been rolled out for the vote. All 400,000 of Afghanistan’s police and soldiers were said to be on duty for the election.
In parts of the capital voters could be seen queuing an hour before polls opened.
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 were also reports elsewhere of several polling centers not receiving ballot materials in time.
Independent Election Commission chairman Ahmad Yousuf Nouristani urged all Afghans to vote, as he cast his ballot live on television.
Traffic was prevented from entering the Afghan capital from midday on Friday, with police checkpoints erected at every junction.
International observers are increasingly 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.
Afghans have been barred from sending text messages until polls close at 16:00 on Saturday to prevent the service from being used for last-minute campaigning.
But there are still concerns about ballot stuffing and 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.
On Saturday the interior ministry said two police were arrested in Wardak province for stuffing ballot boxes.
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 Abdullah has fought a polished campaign, Dr. Ashraf Ghani has strong support among the new urban youth vote and Dr. Zalmai Rassoul is believed to favored by Hamid Karzai.
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 May 28.
A poll conducted by the Free and Fair Election Foundation found that more than 75% respondents planned to vote, even though faith in the electoral process was said to be decreasing.
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