Millions of voters turned out on 18 September to cast ballots for the 249-seat Wolesi Jirga lower house of parliament, as well as for 34 provincial councils.
At least 14 people, including a French soldier, were reported killed in a spate of violence, but no major attacks were reported against voters.
No official figures were available, but officials said they believed a significant proportion of the more than 12.4 million registered voters went to the polls.
Preliminary official results are not expected until early October.
U.S. President George W. Bush, in a written statement, congratulated Afghans for a "successful" vote that Bush said marked a major step toward Afghanistan's development as a democratic state governed by the rule of law.
British Prime Minister Tony Blair said he admired the courage of the candidates who stood for office, including the many women. Blair said the Afghan people have once again shown their determination to build a better future.
NATO Secretary-General Jaap de Hoop Scheffer said the vote was another major step on Afghanistan's road to recovery, peace, and stability.
(AP/Reuters/AFP)For RFE/RL's full coverage of the parliamentary elections in Afghanistan, see "Afghanistan Votes"