Maumoon Abdul Gayoom, the 71-year-old incumbent, faces his toughest critic Mohamed "Anni" Nasheed, 41, after failing to win an outright victory in the first round on October 8.
"Polling started at the scheduled time -- 9.00 am (0400 GM)," Elections Commission spokesman Mohamed Tholal said, adding that the 209,000 electorate would vote over an 11-hour period.
Residents in the capital island Male lined up an hour before booths opened and there were nearly 50 people ready to vote at the Ameenia Collage polling centre where President Gayoom was also due to vote later in the day.
Gayoom's rival Nasheed was due to vote around noon at the nearby Telecom Building polling centre, his spokesman said.
Unarmed Maldivian police guarded the area and police were seen on the narrow streets of the highly congested capital where 90,000 people are crammed in an area of just under 2.
5 square kilometres (one square mile).
Tholal said voting was also taking place in Britain, India, Malaysia, Sing