Taliban spokesman Zabiullah Mujahid said in a statement that their fighters attacked at least 16 polling stations throughout the country, but government official could not confirm this.
The Taliban have repeatedly warned Afghans not to go to polling stations, saying they would slit the throats and chop off fingers of anyone who votes.
Initial turnout was about a third or a fourth of the turnout in the 2004 elections, possibly also out of fear of attacks, which in Kabul often occur in the early hours of the day, witnesses said.
People were afraid of attacks, but there was hope that turnout would pick up later in the day, said political analyst Haroon Mir.
President Hamid Karzai, the frontrunner, who cast his vote at a polling station near the presidential palace early in the day, urged people to take part in the elections, his office said in a statement.
'Hamid Karzai requested Afghan people to come out of their houses and come to polling stations and bravely elect their president and provincial councils,' the presidential statement said.
There were unconfirmed reports about attacks in other parts of the country, but fearing a low turnout, the Afghan government requested all national and international media organisations not to report violence on election day.