Voters are also electing 420 provincial council members for the country's 34 provinces.
More than 270,000 election observers, including 2,000 foreign observers, are 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.
While Karzai led in recent opinion polls, he is not expected to receive more than 50 percent to win the elections outright. If no candidate posts a first-round majority, a run-off would be held around first week of October.
Taliban militants vowed to disrupt the vote and have threatened to slit the throats and chop off fingers of anyone who votes on Thursday.
Afghan and NATO military officials offered assurances that more than 100,000 international troops and around 200,000 Afghan forces were on high alert and were prepared to neutralise any attack that might be mounted by the Taliban.