The two leading candidates in Afghanistan's presidential election both say they have won their country's top political post, a day after millions of voters cast ballots in defiance of Taliban threats.

Limited results won't be known until Tuesday. But the campaign teams of incumbent Hamid Karzai and his top competitor, ex-foreign minister Abdullah Abdullah, both claimed Friday that they had won the most votes.

"My advice is that all the candidates should be patient and wait until the results go through the proper channels and results are announced," said the country's chief electoral officer, Daoud Ali Najafi. Ballots have been counted at individual polling stations and are en route to Kabul, election officials said.

Thursday's presidential poll was the second since the U.S.-led invasion toppled the Taliban regime there nearly eight years ago.

While millions of Afghans cast ballots, risking being attacked by insurgents, turnout still appeared to be much lower than the 2004 election. A senior election official said he expects that 40 per cent to 50 per cent of Afghanistan's 15 million registered voters participated in the election, significantly less than the 70 per cent who cast votes in the previous presidential poll.

If neither of the two leading candidates wins more than 50 percent of the ballots, a second round of voting will be held to determine who will lead the war-torn country.

Karzai's team claimed the president had won enough votes to avoid a runoff. Campaigners for Abdullah said they were investigating claims of fraud in the south of the country, areas where Karzai is expected to do well.

"As far as my campaign is concerned, I am in the lead, and that's despite the rigging which has taken place in some parts of the country," Abdullah told The Associated Press. He accused government officials of interfering with ballot boxes and blocking monitors from inspecting them.

U.S. President Barack Obama has made the election a key component of American strategy for reconstructing the country. With a high enough turnout, the hope was that Afghans would consider the election to be legitimate, and send a symbolic message that they reject the insurgency.

But expectations for the election were low because of the declining credibility of the country's leadership, as well as Taliban threats to attack voters or anyone running voting stations.

At least 26 people were killed in election-related violence. In southern Taliban strongholds, where the risk of violence was greater, a lower voter turnout would hurt Karzai, boosting Abdullah's chance of reaching the 50 per cent threshold or forcing a second round of voting.

"Exit polls might offer preliminary results within a few days," said CTV's Janis Mackey Frayer, from Kabul. "However, it could take weeks for officials to clear what they deem to be serious complaints. There were nearly 400 going into the vote, before a ballot was even cast."

The next president will serve a five-year term and will face serious crises, including deteriorating security in the country, a rising insurgency, pervasive corruption and a thriving opium industry.

The final official results won't be known until early September.

With files from The Associated Press