But observers have hailed this election a success, after voting passed off relatively peacefully amid threats of Taliban attacks.
The UN said the vast majority of polling stations were able to function.
However, Afghanistan's Independent Election Commission (IEC) said on Friday that 11 people had been killed by insurgent attacks while trying to organise the election.
Allegations of ballot box tampering and block voting are also threatening to overshadow the result. Abdullah Abdullah told the BBC he had complained to the electoral commission about alleged voting irregularities by supporters of Mr Karzai in the southern province of Kandahar. Mr Karzai has not commented on the claims.
And, in a sign of the ongoing difficulties facing the next president, the UK government announced the deaths of two British soldiers, killed by an explosion while on routine foot patrol in Helmand province.
The deaths happened on Thursday but were not connected to the election, the Ministry of Defence said.
Deen Mohammad, the campaign chief for Hamid Karzai, said they predicted victory after reports from nearly 29,000 monitors they had at polling stations across the country.
AT THE SCENE
Hafizullah Fayaz BBC Uzbek/Afghan service, Mazar-i-Sharif
Security men are still guarding this girls' school-turned-polling station. One said they would stay until all the counting was done and the ballot boxes had gone to the city's main election centre.
Counting for the presidential poll was completed in many of Mazar's voting centres late on election night.
The results are hanging on the walls inside the polling stations - sheets of paper with the candidates' names and number of votes next to them.
Not many voters are around to check on the results. Most of the delegates of the main challengers seem happy with the count, though some have complained of problems with the indelible ink used to mark the fingers of voters who cast their ballots.
Early results at six polling stations here do not give any candidate more than 50%.
"Initial results show that the president has got a majority," he told Reuters news agency. "We will not go to a second round. We have got a majority."
But a spokesman for Abdullah Abdullah was quick to play down the Karzai camp's claims.
Fazl Sangcharaki said the results from his observers at polling booths around the country suggested Abdullah Abdullah had won 63% of the vote to Hamid Karzai's 31%.
"This is not a final result," he told the AFP news agency. "We are still receiving more results from our people on the ground. We might be done by tomorrow."
The 6,200 polling stations are required to make public the results as they count them, but Afghan election officials refused to confirm either candidates' claims.
Instead, they asked the campaign teams to stay calm and refrain from speculating on the results. "We cannot confirm any claims by campaigning managers," said Zekria Barakzai of the IEC. "It's the job of the election commission to declare the results. They should be patient."
Was Afghanistan's election fair?
Official results had not been expected for a couple of weeks, but the IEC confirmed on Friday that ballot counting was over for the presidential election in all parts of the country and the result could come in the next few days.
Pre-election opinion polls suggested Hamid Karzai was leading the field of 30 candidates, but might face a second round run-off with Mr Abdullah.
If neither candidate wins an outright majority of 50%, then the vote is expected to go to a second round in October.
COUNTING THE VOTES
Counting began after polls closed at 1700 local time on Thursday
Votes counted by hand at each of the 6,200 polling stations
Polling stations are required to post their results immediately, to prevent fraud
Candidates' representatives are also given immediate access to results
The counting appeared to be completed by Friday lunchtime, with official returns due over the weekend
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