An expert panel is still reviewing allegations of electoral fraud levelled by other candidates, and it will take several more days for an official announcement declaring the winner.
According to preliminary results released on Sunday, Karzai has received 4,105,122 votes, more than half of the estimated 8,114,071 valid votes cast in the 9 October vote. He must get more than 50% to win the election outright and avoid a run-off against his closest challenger.
About 7,473,059 valid votes - or just more than 92% of the total - have been counted so far, with Karzai currently at 54.9%, 38.5 points ahead of his nearest rival, former education minister Yunis Qanuni.
Qanuni, conceded defeat on Sunday with less than 6% of the vote count remaining.
Former education minister Yunis
Qanuni was Karzai's main rival
A spokesman said Qanuni would accept Karzai's victory despite irregularities in the elections.
"We will accept the result because we do not want to drag the country into crisis," Sayyid Hamid Nuri said.
Hamid Ilmi, Karzai's campaign spokesman, said Sunday's figures supported optimism that the interim leader would triumph when the final results are released.
"I'm going to see his excellency this evening to see when to start the celebrations," said Ilmi. "We were up against 17 candidates, but the people were behind us. We will sleep soundly tonight."
Ethnic Hazara chieftain Muhammad Muhaqiq, who is currently running third at 11.7%, refused to concede.
"It's too early to judge the result now," he said. Another main rival, Abd al-Rashid Dustum, has already accepted Karzai as the winner.
It is possible that more votes were actually cast than the current estimate, but barring a wildly incorrect estimate on votes cast coupled with the near impossibility of all the remaining votes going to other candidates, any changes would not be enough to drop Karzai under the 50% mark.
An expert panel is still reviewing
allegations of electoral fraud
The estimate of the total number of valid votes cast is based on a projection given by the joint UN-Afghan election board of the total turnout, adjusted to deduct the forecast proportion of spoiled ballots.
Investigation results awaited
Electoral officials have said they will not call the election until the investigation into the fraud allegations and the vote count are both complete.
Sultan Bahin, a spokesman for the election board, reiterated that it will not announce the official results until both the count and the investigations are complete.
"I hope it won't take too long - maybe two or three days more," he said.
Karzai has served as the country's interim leader since US forces drove out the former ruling Taliban government in late 2001 for harbouring Usama bin Ladin.