Voting in the second round of Afghanistan's presidential election has ended with millions turning out to cast their ballots, despite attacks that left at least 46 people dead.

Fighters launched at least 150 attacks with rockets, explosives and gunfire during Saturday's voting, killing at least 20 civilians, along with a further 11 police and 15 army personnel, the Interior Ministry said.

"Election security was better than the first round despite level of threats being higher," Interior Minister Omar Daudzai told reporters. "People voted to reject the militants. There were some casualties on our side, but the enemy has failed."

Daudzai said about 60 fighters were also killed.

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Despite the violence, the election commission said initial estimates showed that more than 7 million Afghans voted, which would be equivalent to the first round on April 5.

That would be a turnout of about 60 percent of Afghanistan's 12 million eligible voters.

The runoff pitted former Foreign Minister Abdullah Abdullah against ex-World Bank economist Ashraf Ghani after neither secured the 50 percent majority needed to win outright in the first round. 

'Fingers cut off'

Taliban fighters had vowed to disrupt the election, which they have condemned as a US-sponsored charade.  

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In Herat province, 11 voters were treated in hospital after allegedly having their ink-stained fingers cut off by Taliban fighters. 

"While we were on our way to homes we were stopped by Taliban, who took us to their village where they cut off our fingers," one of the men told Reuters.

Observer groups said the balloting was relatively smooth, although both candidates and observers said they had evidence of fraud ranging from ballot box stuffing to proxy voting.

Several polling stations also opened late or failed to open at all because of security concerns, and many voters complained of ballot shortages.

About 330 voting centres ran out of ballot papers, sparking minor protests by disgruntled voters. The election commission said additional materials were later distributed and calm was restored. 

Abdullah secured 45 percent of the first-round vote with Ghani on 31.6 percent, after coming out top of an eight-man field.

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

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

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

Source: Agencies