Afghans celebrated a largely peaceful election on Saturday, as turnout exceeded predictions despite Taliban threats to disrupt the vote to choose President Hamid Karzai's successor.

Long queues of voters waited throughout the day outside many of the 6,400 polling centres before the prolonged process of counting began, with preliminary results not due until April 24.

Whoever emerges victorious must lead the fight against the Taliban without the help of US-led combat troops, and also strengthen an economy that currently relies on declining aid money.

The country faces a testing few months as it undergoes its first democratic transfer of power, and many Afghans fear a repeat of the fraud scandals that marred the last presidential election in 2009.

If no candidate wins more than 50 percent in the first round, a run-off is scheduled for late May.

There were no major militant attacks during polling, and organisers described the election as a huge success, despite complaints that a shortages of ballot papers had denied some citizens the right to vote.

"Today's election and massive participation of the people have taken Afghanistan a few steps forward to peace, stability and development," Karzai said in an address to the nation.

"This was a major effort of the people, our security forces, and all the officials who had a role in holding the election."

US President Barack Obama called the vote "critical to securing Afghanistan's democratic future, as well as continued international support".

"Millions of Afghan men and women took to the polls today with courage and commitment," US Secretary of State John Kerry said in a statement.

"This is their moment."

NATO chief Anders Fogh Rasmussen praised the "enthusiasm" of voters and the "outstanding job" by Afghan security forces.

"This has truly been an election led by Afghans, secured by Afghans, for the future of Afghans," he said.

British Foreign Secretary William Hague called the election a "great achievement", and urged parties to show "patience and respect" during the count.

The final turnout could exceed seven million, the head of the Independent Election Commission (IEC), Ahmad Yusuf Nuristani, said, though this was a preliminary estimate and may change. Initial predictions in 2009 proved inaccurate.

Around 13.5 million people were eligible to vote, putting the estimated turnout above 50 percent -- a significant increase on 2009, when only around a third of voters cast ballots.

"Open race"

There is no clear favourite among the front-runners to succeed Karzai -- former foreign minister Zalmai Rassoul, Abdullah Abdullah, who was runner-up in the 2009 election, and former World Bank academic Ashraf Ghani.

The open nature of the race coupled with a massive security operation to thwart Taliban attacks may have contributed to the high turnout.

The Taliban had urged their fighters to target polling staff, voters and security forces, but there were no major attacks reported during the day.

In Kabul, hit by a series of deadly attacks during the election campaign, hundreds of people lined up outside polling centres to vote despite heavy rain and the insurgents' promise of violence.

"I'm not afraid of Taliban threats, we will die one day anyway. I want my vote to be a slap in the face of the Taliban," housewife Laila Neyazi, 48, told AFP.

One blast in Logar province, south of Kabul, killed one person and wounded two, according to Mohammad Agha district chief Abdul Hameed Hamid.

Interior Minister Omar Daudzai said four civilians, nine police and seven soldiers had been killed in violence in the past 24 hours, and added that many attacks had been foiled, without giving further details.

Attacks or fear of violence had forced more than 200 of a total 6,423 voting centres to remain closed.

The day before the poll, Associated Press photographer Anja Niedringhaus was shot dead by a police commander in eastern Khost province.

She was the third journalist working for international media to be killed during the election campaign, after Swedish journalist Nils Horner and Sardar Ahmad of Agence France-Presse.

Fresh start?

Afghans have taken over responsibility for security from US-led forces, and this year the last of the NATO coalition's 51,000 combat troops will pull out, leaving local forces to battle the resilient Taliban insurgency without their help.

The country's third presidential election will bring an end to 13 years of rule by Karzai, who has held power since the Taliban were ousted in 2001.

Massive fraud and widespread violence marred Karzai's re-election in 2009, and a disputed result this time would add to the challenges facing the new president.

The election may offer a chance for Afghanistan to improve relations with the United States, its principal donor, after the mercurial Karzai years.

Relations fell to a new low late last year when Karzai refused to sign a security agreement that would allow the US to keep around 10,000 troops in Afghanistan to train local forces and hunt Al-Qaeda.