Both Afghan president Hamid Karzai and his main rival in the presidential election have claimed victory.
The incumbent president's campaign manager says Hamid Karzai, who is hoping for a second term, has secured an outright majority. He says the estimate of victory is based on reports from its monitors at polling stations.
However a spokesman for his main challenger Abdullah Abdullah dismissed the claim, and said Dr Abdullah was in the lead.
If no candidate won an outright majority, a second round of voting would be held in October.
Electoral officials estimate the turnout at 40% to 50%, the BBC reports.
Vote counting began immediately after polls closed on Thursday and official results are expected to be announced in about two weeks.
Sporadic election day violence
Mr Karzai says the millions of Afghans who went to the polls had "dared rockets, bombs and intimidation" in order to vote.
The Afghan government says nine civilians and 14 members of the security forces were killed in a total of 135 incidents countrywide on polling day.
Rockets fell on towns, especially in the south and east, and two gunmen wearing suicide vests were killed in a gun battle in Kabul, but the violence in the morning tapered off as the day went on.
In Washington, United States President Barack Obama hailed the conduct of the election and vowed to press on with his strategy, which has involved sending thousands of additional troops to the country.
"We had what appears to be a successful election in Afghanistan, despite the Taliban's efforts to disrupt it," Mr Obama said from the White House.
High voter turnout in Bamiyan province
There were sporadic bombings in Bamiyan province in northern Afghanistan, where a New Zealand provincial reconstruction force is stationed.
Group Captain Greg Elliott says the New Zealand contingent's 140 troops were out in the district on polling day providing general security.
He says there was high voter turnout despite intimidation and insurgent attacks. Group Captain Elliott says while some Afghans want a return to anarchy, many are determined that the first fully contested election in the country's history will be a success.
