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Taliban militants, who had threatened to disrupt the vote, launched low-level attacks in which at least 46 people were killed across the country.
More than seven million people turned out to vote, election officials said.
Voters are choosing between former Foreign Minister Abdullah Abdullah and ex-World Bank economist Ashraf Ghani.
This election will be the first time that power in Afghanistan has been democratically transferred.
The Taliban had said they would target voting, and there were concerns that fraud could produce a disputed result.
The Afghan interior minister earlier said there had been 150 attacks. BBC said it had seen more violence than in the previous round, but most incidents were relatively low level.
Election commission chief Ahmad Yousef Nooristani said fewer than 200 of the 6,365 polling stations were unable to operate because of security concerns.
Of those who turned out to vote, 38% were women and 62% were men, he said.
Mr Nooristani also said there had been some complaints of irregularities which would be investigated, but did not give further details.
Presidential candidate Abdullah Abdullah thanked "the whole nation of participating in the election" and called for a full investigation in the allegations of fraud.