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

(Agencies)

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