Electoral officials have urged patience, saying partial results could come as early as Sunday, but it is likely to be at least a week before a complete picture emerges.

More than 1,200 complaints had been received by the Election Complaints Commission (ECC) by Sunday morning, spokesman Nadir Mohsini said.

"Complaints include late opening of polling centres, shortage of ballot papers, encouraging of voters to vote for certain candidates and mistreatment of some election officials," he added.

Although there are eight candidates for president, only three are considered frontrunners - former foreign ministers Abdullah Abdullah and Zalmai Rassoul, and former Finance Minister Ashraf Ghani Ahmadzai.

Analysts say Dr Abdullah has fought a polished campaign, Mr Ghani has strong support among the new urban youth vote, and Dr Rassoul is believed to favoured by Mr Karzai.

Dr Abdullah, who pulled out of the 2009 vote before the second round amid allegations of irregularities, hailed Saturday's poll as a success. However, he complained that many voters had been deprived of their right to take part because of a lack of ballot boxes.

The UN Security Council has issued a statement applauding preparations for the vote, and urging the candidates and their supporters to "respect the electoral institutions and processes".

Thijs Berman, the head of the European Union's election assessment team in Kabul, praised the courage of Afghan voters.

"This in itself is a victory over violence and a victory over all those who wanted to deter democracy by threats and violence," he said.

Mr Karzai, barred by the constitution from seeking a third term, said after polls closed: "Despite the cold and rainy weather and possible terrorist attack, our sisters and brothers nationwide took in this election and their participation is a step forward."

US President Barack Obama said in a statement: "We commend the Afghan people, security forces, and elections officials on the turnout for today's vote."

UK Foreign Secretary William Hague said in a statementement: "It is a great achievement for the Afghan people that so many voters, men and women, young and old, have turned out in such large numbers, despite threats of violence."

Nato military alliance chief Anders Fogh Rasmussen said the elections were "a historic moment for Afghanistan".

Nato has co-ordinated much of the work of foreign forces in Afghanistan - most of them US and British troops - in a mission that will end this year.

Meanwhile, the Afghan authorities say at least 13 suspected Taliban insurgents were killed on Saturday in separate American drone attacks in the east of the country.

In the first attack, seven militants died in the district of Ghaziabad in Kunar province, near the border with Pakistan. Later, after nightfall, six Taliban militants were killed in the same district.

The Taliban carried out several attacks on polling stations and security forces in Kumar province during the presidential poll on Saturday.