Hamid Karzai, the Afghan president, said the election was conducted "successfully" throughout the country despite Taliban attacks that resulted in deaths of Afghan security forces and civilians.
"The Afghan people defied rockets, bombs and intimidation and came out to vote, that is great," Karzai - the frontrunner of the 30 candidates - told a news conference in his fortified palace.
"Despite problems and intimidation, the elections ended successfully," he said, adding that armed groups conducted attacks in 15 of Afghanistan's 34 provinces.
Afghanistan's election authority, which extended the voting until 5pm Kabul time (12:30 GMT), said it was launching an investigation into complaints of irregularities.
Allegations from candidates included claims ink used to mark voters' fingers could be scrubbed off and that election officials had told people to vote for the incumbent president, election commission officials said.
|Electoral workers count the ballots at a polling station in Herat [AFP]
The main challenger, ex-foreign minister Abdullah Abdullah, released a statement detailing about 40 incidents of alleged irregularities, most saying that officials had pressured voters into choosing Karzai.
Ramazan Bashadost, another presidential candidate, said he had been able to remove the ink with cleaning fluid, Azizullah Lodin, the chief of Independent Election Commission (IEC), told reporters.
There were also claims voting centres did not have enough ballot papers.
Voter turnout appeared to be down during the morning, particularly in the south of the country, but picked up in the afternoon.
Officials praised the turnout in many areas, with queues being reported despite sporadic mortar and rocket attacks, a number of which apparently targeted polling stations.
"The turnout is very good," Zekria Barakzai, deputy chief electoral officer, said.
Election observers seemed more pessimistic, though, suggesting that less than 50 per cent of the electorate may have taken part.
About 17 million people were eligible to vote in presidential and provincial elections, with 6,500 polling stations open in 364 districts across the country.
Before the polls had closed, Ahmad Wali Karzai, head of the Kandahar provincial council and brother of Hamid Karzai, said that there had been "a very good turnout" across the province.
"There were so many explosions last night and this morning before the polling stations opened," he told Al Jazeera.
"We had serious security challenges, but despite all the challenges we have had a very good turnout and the people of Kandahar came out bravely and voted.
"We are very happy and satisified with the results."
The government regained control of Kandahar city last year, but the south of Afghanistan is still the Taliban heartland.
In the north of the country, Al Jazeera's Hashem Ahelbarra, reporting from the city of Mazar-e-Sharif, said that officials there had also been postive about the turnout.
"We have spoken to election commission officials in different provinces of the north of Afghanistan and we were told that in six provinces out of the nine in the north voter turnout was really high," he said.
"The north of Afghanistan has been described as relatively calm ... and here in Mazar-e-Sharif we haven't seen any incidents so far."
Kabul, the capital, appeared quiet throughout Thursday with shops and businesses closed and police checking the few cars on the roads.
James Bays, Al Jazeera's correspondent in Kabul, said: "I spent the last hour of official voting in one polling station in the capital where I saw only one voter in all that time.
"It is very, very slow."
Hamid Karzai had urged voters to defy the Taliban as he cast his ballot in a boys' school adjoining the presidential palace in Kabul.
"I request my dear countrymen to come out and cast their vote to decide their future," he said. "Vote. No violence."
|Opinion polls suggest Hamid Karzai could face a run-off against Abdullah Abdullah [Reuters]
Abdullah Abdullah, a former foreign minister and Karzai's closest challenger, also had a similar message.
"I am happy that a lot of people are participating in this election despite security concerns and concerns about fraud in the election," he said.
Karzai needs to secure 50 per cent of the vote to win in the first round, but opinion polls before the election indicated that he was likely to face a run-off against Abdullah.
The Taliban had demanded that Afghans boycott the polls, threatening to cut off the fingers of those who voted and launch attacks on polling stations.
But Kai Eide, the UN special envoy to Afghanistan, said he was happy that the security efforts of the Afghan police and military, as well as the Nato-led forces, appeared to have been able to prevent any major violence.
"The kind of spectacular attacks that we were warned about have not happened," he said.
"The day is still not over but I must say I am pleased to see that so far the elections have been going on quite well."