With turnout higher than expected after a largely peaceful day of voting, Washington hailed the polls as a "significant step" for the country's democracy, commending "the voters, electoral bodies and security forces for their commitment to the democratic process".
"These elections are a significant step forward on Afghanistan's democratic path, and the courage and resolve of the Afghan people to make their voices heard is a testament to the importance of these elections to securing Afghanistan's future," the White House said.
Ahead of the ballot, which decides the next president of the country ahead of the withdrawal of NATO troops later this year, the Taliban had threatened to kill voters and officials, saying the election was an American plot "to impose their stooges".
Polling day saw no major attacks in cities, but there were at least 150 minor attacks -- including a Taliban rocket that hit a house near a polling station, killing five members of the same family.
Eleven voters in the western province of Herat had their fingers -- which were dipped in ink to register their ballot -- cut off by insurgents, Deputy Interior Minister Ayoub Salangi said on his Twitter account.
The polls result, due out next month, will confirm whether former foreign minister Abdullah Abdullah or ex-World Bank economist Ashraf Ghani will lead Afghanistan into a new era of declining international military and civilian assistance.
The two candidates came top of an eight-man field in the April first-round election, triggering the run-off as neither reached the 50 percent threshold needed for outright victory.
Abdullah secured 45 percent of the vote with Ghani on 31.6 percent.
Counting the ballot will take weeks. The preliminary result is due on July 2 and a final result on July 22.
- Fraud fears linger -
The United Nations also praised the elections, congratulating the "courageous" Afghans who set out to cast their ballots in the face of Taliban threats.
"With the same determination, resilience and courage the world saw in the first round of elections, the people of Afghanistan today once again decided to take their destiny in their own hands and demonstrate their desire for a peaceful, prosperous, and united Afghanistan," the UN Secretary-General's Special Representative for Afghanistan, Jan Kubis, said.
While high turnout may lend legitimacy to the winner if the gap between the two candidates is clear, a close count could mean a contested outcome.
Both candidates swiftly alleged fraud after the closure of the polls Saturday.
"We know there has been fraud, you have seen it, we have seen it," Abdullah said.
Ghani called for a full investigation into vote-rigging, saying "unfortunately there were cases of security forces involved in fraud, we have the evidence".
A smooth handover in Afghanistan's first democratic transfer of power would be a major achievement for the 13-year US-led effort to establish a functioning state after the depredations of the Taliban era.
President Hamid Karzai, who has ruled Afghanistan since 2001 and was re-elected in a 2009 vote marred by ballot-box stuffing, is constitutionally barred from a third term in office.