Taliban insurgents launched a spate of attacks that killed dozens in the run-up to the vote, which they brand as a US-backed sham but there was no word of violence as voting got under way.
About 12-million people are eligible to vote in the election. There are eight candidates contesting, with former foreign ministers Abdullah Abdullah and Zalmay Rassoul and former finance minister Ashraf Ghani the favourites.
Hamid Karzai, the incumbent, is not allowed to run for the presidency again by the constitution. But, after 12 years in power, Karzai is widely expected to retain influence through politicians loyal to him.
More than 350 000 Afghan troops have been put on duty to thwart attacks on polling stations and voters. The capital, Kabul, has been sealed off from the rest of the country by rings of roadblocks and checkpoints.
Most people expect the election will be better run than the chaotic 2009 vote that handed Karzai a second term amid massive fraud and ballot stuffing.
But it could take months – perhaps until October – for a winner to be declared at a time when the country desperately needs a leader to stem rising violence as foreign troops prepare to leave.
Any delay would leave little time to complete a pact between Kabul and Washington to keep up to 10 000 US troops in the country beyond 2014, after the bulk of the American force, which currently stands at around 23 500, has pulled out.
Karzai has rejected the agreement, but the three frontrunners to succeed him have pledged to sign it. Without the pact, far weaker Afghan forces would be left on their own to fight the Taliban, who have mounted an increasingly bold and violent campaign against the Kabul government.
Uncertainty over the outcome could also stall crucial foreign aid and economic reform, foment ethnic tensions and leave a political vacuum in which the Taliban could gain ground.
The Taliban have warned civilians they would be targeted if they try to vote on Saturday.
A veteran Associated Press photographer was killed and a senior correspondent of the same news agency was wounded on Friday when a policeman opened fire on the two women in eastern Afghanistan as they reported on preparations for the poll. – Reuters