The voting was relatively peaceful despite a series of rocket barrages and other scattered attacks that Interior Minister Mohammad Umar Daudzai said killed 47 people, including 20 civilians and an election commission worker. He said 60 militants were killed.
Later on Saturday a minibus hit an improvised explosive device in the northern Samangan province. The blast killed six women, one child and four men in the provincial capital Aybak, said Sediq Azizi, spokesman for the provincial governor.
Azizi said four of the victims were employees of the election commission. It was not immediately clear if they were the target of the explosion.
In a separate incident, the Taliban cut off the index fingers of 11 civilians on Saturday in western Herat province to punish them for voting, police spokesman Raoud Ahamdi said.
The United Nations Assistance Mission to Afghanistan condemned the mutilations in Herat.
"Like millions of their countrymen and women, these ordinary Afghans were exercising their fundamental right to determine the future path of their country through voting and not through violence and intimidation. By their vote, they already defeated those who promote terror and violence," said Jan Kubis, the U.N. special representative.
In the southern Kandahar province, police said they raided a building Sunday that had been occupied by the Taliban the day before, setting off clashes in which police shot dead two would-be suicide bombers but were unable to prevent another two from blowing themselves up and killing three policemen and wounding another two.
Afghans braved threats of violence and searing heat Saturday to vote in the presidential runoff, which likely will mark the country's first peaceful transfer of authority, an important step toward democracy as foreign combat troops leave.
Abdullah, who emerged as the front-runner with 45 percent of the vote in the first round, faced Ahmadzai, an ex-World Bank official. Neither garnered the majority needed to win outright. The Independent Election Commission said initial estimates showed that more than seven million Afghans voted Saturday, or about 60 percent of the country's 12 million eligible voters. The first round on April 5 saw a similar turnout.