The polling stations were equally quiet in the morning. Visits to three polling stations over the first three hours of voting revealed no more than 80 people and only one woman turning out as militants fired rockets and exploded bombs in Kandahar, beginning at 3 a.m. (2230 GMT Wednesday).
At least 10 blasts were heard, and police said they discovered and defused 12 homemade bombs.
The explosions waned in the afternoon, and voter numbers rose.
Defence Ministry spokesman Aahir Azimi said Thursday afternoon that reports from the provinces showed that the feared violence had not materialised and he described the conditions in Afghanistan as 'normal'.
Thomas Ruttig, an election observer in the south-eastern province of Paktia, said he had expected worse.
'I drove out with a bit of fear that has not proven true,' said the co-director of the Afghanistan Analysts Network, an independent policy research organization.
However, he also spoke of a 'very mixed picture', saying turnout in districts near the provincial capital, Gardez, was low although those areas were quiet while districts farther from Gardez were hit by rockets. The Taliban blocked roads in one district to prevent voters from reaching polling stations, Ruttig said.
Turnout was good in the provincial capital of Gardez until a suicide bomber was killed at a polling station there, he said. Azimi told Tolo television that police shot the bomber before he could enter the polling centre.
Two other suicide bombers were arrested trying to enter polling stations in the northern province of Takhar, provincial police chief Ziauddin Mahmoodi said.
Meanwhile, in the northern province of Baghlan, a district police chief was killed when militants attacked a police post, a security source in the province said.
Polling stations opened at 7 a.m. (0230 GMT), and voting is to continue until 4 p.m. (1130 GMT). Initial results were expected about 48 hours after the polls close, the Independent Election Commission said.
Voters were electing not only a president but also 420 provincial council members for the country's 34 provinces.
More than 270,000 election observers, including 2,000 foreign observers, were overseeing the balloting at more than 6,500 polling centres while the commission said it was unable to open voting stations in nine districts that remain outside government control.
Although Karzai led in recent opinion polls, he was not expected to receive more than 50 percent of the vote to win the election outright. If no candidate posts a first-round majority, a run-off would be held the first week of October.