Afghan and international officials hailed Sunday's elections as a major success in the country's march toward democracy, but chief electoral officer Peter Erben said reports from about one-third of the polling stations indicated a turnout of just over 50 percent.
International observers said that Taliban violence, which has killed more than 1,000 in the past six months, may have scared voters away.
Results were not expected for more than a week.
The government and its Western backers hailed the first elections for a national assembly in over 35 years as a strong show of defiance in the face of Taliban threats and determination to bring stability after decades of war and chaos.
"Afghanistan should be satisfied with the turnout in yesterday's election," Erben said. He said it compared well with elections in other postwar countries.
Karzai praised voters — who cast ballots in schools, mosques and even desert tents — for coming out "in spite of the terrorism, in spite of the threats." In New York, U.N. Secretary-General Kofi Annan said the election showed "the clear determination of the Afghan people to pursue the peaceful and democratic development of their nation."
President Bush called the vote successful and a major step forward, commending "the tremendous progress that the Afghan people have made in recent years."