KABUL: 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.

Turnout was 7 million out of 12 million eligible voters, or about 58 per cent, according to preliminary estimates in what will bring the first-ever democratic transfer of power in a country plagued by conflict.

The Independent Election Commission ordered voting to be extended by at least an hour, with ballot papers being dispatched where they were needed.

Also see: Afghan elections: As it happened

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 per cent 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.”

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 per cent – a significant increase on 2009, when only around a third of voters cast ballots.

Related: Infographic: Understanding the Afghan elections

Of the eight candidates contesting the presidency, the three frontrunners to succeed Karzai - who is barred by the constitution from running again – are former foreign ministers Abdullah Abdullah and Zalmai Rassoul and former finance minister Ashraf Ghani.

A smooth election with a high turnout is good news for Afghanistan's Western backers who are watching the vote closely in order to decide whether to continue to extend billions of aid desperately needed to support Afghanistan's ailing economy.

It was not immediately clear how widespread the shortage of ballot papers was around the country. Afghanistan has 12 million eligible voters, and officials say there were 15 million ballot papers printed.

In Kandahar, a Taliban stronghold and Afghanistan's second city, ballots had run out at the majority of polling stations in the city, according to a spokesman for the governor's office.

“Due to the mismanagement of election commission in Kandahar, voting materials in the majority of polling stations have run out,” said Dawakhan Menapal, the spokesman.

One young, angry voter, Mohammad, said he was upset because he was unable to vote.

“I came here at 8 a.m. to this polling station to select our candidate, it's 11:30 and the election workers has told us that the election papers have run out and you should go to a different polling station,” he said. “People have crushed their voting cards and thrown them away.”

There was no official on turnout, but at the last election in 2009, the turnout of 4.6 million was regarded as low.

Because of Afghanistan's difficult terrain, it will take weeks for officials to gather ballot boxes from around the country and count the votes. Official preliminary results from the Saturday vote are not expected until late April– AFP/Reuters