KABUL: Afghans defied Taliban threats by voting Saturday in a second-round presidential election, as US-led combat troops wind down a 13-year war that has failed to defeat the insurgents.

No major attacks were reported in the first hours of voting, though the Taliban claimed responsibility for two rockets exploding near Kabul airport causing no casualties.

The run-off election will decide whether former foreign minister Abdullah Abdullah or ex-World Bank economist Ashraf Ghani leads the country into a new era of declining international military and civilian assistance.

President Hamid Karzai is due to step down after ruling the country since 2001, when a US-led offensive ousted the austere Taliban regime for sheltering Al-Qaeda militants behind the 9/11 attacks.

"We are very proud to be choosing our favourite candidate," he said after voting.

"Today Afghanistan goes from a transition period toward long-lasting peace and stability."

A smooth handover in Afghanistan's first democratic transfer of power would be a major achievement for the international effort to establish a functioning state after the depredations of the Taliban era.

In the first-round vote in April, the insurgents failed to launch a single high-profile attack and voter turnout was more than 50 percent.

But the stakes were high on Saturday with the Taliban issuing specific threats to target polling stations and widespread fears that electoral fraud could produce a contested result.

UN head of mission Jan Kubis issued a stark warning to candidates' supporters not to resort to the ballot-box stuffing that marred the 2009 election when Karzai retained power.

"Do not commit fraud. Do not use intimidation or manipulation to favour your candidate," he said ahead of polling day.

Abdullah secured 45 percent of the first-round vote with Ghani on 31.6 percent, after investigations into fraud claims from both sides.

The two candidates came top of an eight-man field, triggering the run-off election as neither reached the 50 percent threshold needed for outright victory.

They both cast their ballots in Kabul before dipping a finger in ink to register that they had voted.

On the campaign trail, Abdullah and Ghani offered similar pledges to tackle rampant corruption, build much-needed infrastructure and protect citizens from violence.

"I want someone who can improve our economy, create jobs and improve our lives," said Janat Gul, 45, a shopkeeper voting in Kabul.

"If the economy is good there will be no insurgency, everyone will be busy working, not fighting."

Harsh terrain and poor roads make holding an Afghan election a logistical challenge, with thousands of donkeys used to transport ballot boxes to remote villages.

Counting the ballot will take weeks. The preliminary result is due on July 2 and a final result on July 22.

Ahead of the vote, the Taliban said that polling booths would be targeted by "non-stop" assaults.

"By holding elections, the Americans want to impose their stooges on the people," the insurgents said on their website.

On Saturday, they said their fighters had attacked polling stations around the country, but Afghan officials did not confirm the claims.

Recent weeks have been relatively peaceful except for a suicide blast targeting Abdullah in Kabul last week that left 12 dead.

Afghan officials expressed confidence in the security forces, who have been trained by the US-led military coalition.

"The level of threats is higher compared to the first round, but we have gained far more experience," said interior minister Omar Daudzai.

Ethnic friction is also a concern as Abdullah's support is based among the Tajik minority and other northern tribes, while Ghani is a Pashtun -- Afghanistan's largest ethnic group, which is strongest in the Taliban heartlands of the south and east.

Karzai, who is constitutionally barred from a third term in office, has fulfilled his pledge not to interfere in the election -- in public at least -- though he is tipped to retain influence after handing over power.

His relationship with the US soured badly, and the next president is likely to reset ties by signing a long-delayed pact for some US troops to remain on a training and counter-terrorism mission after this year.

Last month President Barack Obama said that if the pact is signed, 9,800 of the 32,000-strong US deployment would stay in 2015.

The US-led NATO military mission was in a "support role" on Saturday, ready to assist if requested by Afghan authorities.

The coalition has suffered about 3,450 fatalities since operations began in late 2001.

Afghanistan has seen massive changes as billions of dollars of aid money brought rapid development in some cities but only limited improvements in security, women's rights and education.

Priorities for the incoming president will be to stabilise the faltering economy as aid falls, and a fresh attempt to bring peace after decades of war by exploring peace talks with the Taliban.