Militants have cut off the fingers of two voters in Afghanistan's presidential election, according to an election monitoring group, fulfilling a promise the Taliban made before Thursday's vote.

According to the Free and Fair Election Foundation of Afghanistan, the two voters were attacked in Kandahar province shortly after casting their ballots.

Prior to the election, militants had threatened to cut off voters' ink-stained fingers. However, a Taliban spokesperson later denied that such attacks would take place.

In Afghanistan, voters dip their index fingers in purple ink to protect against fraud.

Taliban threats of violence at polling stations and a series of deadly attacks leading up to the vote appeared to scare some Afghans away from the polls, as voter turnout is expected to tally only between 40 and 50 per cent of Afghanistan's 15 million registered voters.

That is considerably less than the 70 per cent who cast their ballots in the previous presidential election.

As ballots were counted Friday, both leading candidates declared victory. President Hamid Karzai declared himself ahead in early voting and would have enough votes to avoid a runoff.

Karzai's main challenger, former Foreign Minister Abdullah Abdullah, said he would likely win enough votes to force a runoff, and that he is in touch with several presidential candidates but not the incumbent. Abdullah would not say whether he has been discussing alliances.

If neither candidate gets 50 per cent of the vote in the first round, a runoff will be necessary.

Preliminary results are expected on Tuesday, but candidates will have to wait until mid-September for a certified final tally.

Karzai was expected to fare well in the south, where he could expect votes from his fellow Pashtuns. However, violence in the south may have kept voter turnout there low, which threatens Karzai's chances of securing a second five-year presidential term.

The final tally also hinges on the results of investigations into claims of voter fraud.

Nader Nadery, the head of the Free and Fair Election Foundation, said his group witnessed election officials pressuring voters to cast their ballots for specific candidates.

The group also noticed ballot-box stuffing, as well as a number of underage voters, Nadery said.

While Nadery's group was present in all 34 Afghan provinces, security concerns limited international monitoring groups to fewer provinces.

Despite threats and allegations of voting irregularities, international observers like former Canadian cabinet minister John Manley say the election was a success.

"In the face of threats and intimidation, millions of people showed up, many candidates participated," said Manley.

He added that millions of Afghans tuned into presidential debates, which "indicates a vital democratic system and one that shows real progress."

The European Union said rocket attacks prevented its observers from getting to some polling stations in southern Kandahar province. The EU eventually got observers to 17 provinces.

"That elections took place at all is a notable achievement," the EU said in a statement. However, threats and violence meant that voting could not be considered free "in some parts of the territory" but that the process so far appeared "good and fair."

With files from The Associated Press