The vote pits former anti-Taliban fighter Abdullah Abdullah against ex-World Bank economist Ashraf Ghani after neither secured the 50% majority needed to win outright in the initial vote on April 5.
Voters were not put off by rockets landing in the capital and other explosions, forming long queues at polling stations before voting began at 7am.
Independent election commission chief Ahmad Yousuf Nuristani sought to reassure voters and observers that the body would ensure the process delivered a legitimate winner.
"We have zero tolerance for fraud and if we detect any case of election staff working in favour of a candidate, they will be sacked immediately," he said.
The process has been fraught with accusations of fraud by both candidates, and many fear a close outcome will make it less likely the loser will accept defeat, possibly dragging Afghanistan into a risky, protracted stand-off over the vote.