The figures came from 10 percent of the more than 27,000 polling sites nationwide - too small a sampling either to draw a conclusion about the outcome or silence criticism that the ballot was marred by fraud and Taliban violence.
The U.S. and its NATO partners had hoped Thursday's election would produce a clear winner with a strong mandate to confront the growing Taliban insurgency, widespread corruption, narcotics and a stagnant economy.
Six other presidential candidates, echoing Abdullah's earlier claims, charged Tuesday that widespread fraud occurred on election day - mostly in Karzai's favor.
The allegations threaten to discredit the eventual winner, stoke violence and cast doubt on the credibility of the Afghanistan democracy at a time when President Barack Obama and other Western leaders are considering investing more resources in an increasingly unpopular war.
Underscoring the crisis, a cluster of vehicle bombs detonated nearly simultaneously near a Japanese construction company in the southern city of Kandahar, killing at least 41 people, flattening buildings and sending flames shooting into the sky. The thundering explosion occurred just after nightfall Tuesday in a district that includes U.N. facilities and an Afghan intelligence office. Kandahar is the spiritual home of the Taliban.
Also in the south, a bombing killed four U.S. service members Tuesday. At least 172 American troops have died in the Afghan war this year - the deadliest since the conflict began in 2001.
The Independent Election Commission announced that Karzai was leading with 40.6 percent and Abdullah was trailing with 38.7 percent of the roughly 525,000 valid votes counted so far. Most of the votes came from Kabul, nearby Parwan and Nangarhar provinces, Kunduz and Jowzjan provinces in the north and Ghor province to the west.
However, the figures did not include votes from 12 of the country's 34 provinces, including some where Karzai was expected to run strong.
In the volatile south, the homeland of Karzai's Pashtun ethnic group, less than 2 percent of the votes in Kandahar province had been counted and no votes in Helmand had been tallied, the commission said.
Karzai would expect to do well in both provinces, suggesting his returns could go higher. However, turnout was believed to have been low in those two provinces because of Taliban attacks and intimidation as well as heavy fighting between the insurgents and U.S.-led forces.
It is unclear whether turnout in the Pashtun south will be enough to significantly offset Abdullah's strength in the mostly Tajik and Uzbek north, which are generally more peaceful.
Abdullah, son of a Pashtun father and a Tajik mother, is widely seen as the northern candidate because of his close association with the northern-based alliance that overthrew the mostly Pashtun Taliban in the U.S.-led invasion of 2001.
Both Karzai and Abdullah had claimed they were leading in early returns, but no official figures have backed those assertions.
The U.S. government urged candidates to wait for more complete results. U.N. officials have also urged caution, fearing that a drumbeat of allegations and recriminations will poison the political atmosphere at a time when the part of society opposed to the Taliban must draw together.
"We call on all parties to refrain from speculation until national results are announced," State Department spokesman Ian Kelly said.
Some Afghans in Kabul expressed weariness with political bickering and hoped a runoff would not be necessary. If neither Karzai nor Abdullah gets more than 50 percent of the vote, the two will face each other in a runoff, probably in October.
"We're tired," said Shirin Agha, 40, who sells melons along a Kabul street. "I'm fed up with all these politicians."
Nevertheless, allegations of vote rigging mounted Tuesday.
Abdullah showed reporters a packet of ballots with an official stamp on the back - used to mark cast ballots - nearly all checked for Karzai. He also showed video of what he said were Karzai supporters in eastern Ghazni province marking dozens of ballots for their candidate, and a picture of a polling site in the south showing people he said were Karzai campaign officials looking over the shoulders of voters.
"If the widespread rigging is ignored, this is the type of regime that will be imposed upon Afghanistan for the next five years and with that sort of a system, a system that has destroyed every institution, broken every law," Abdullah said at a news conference just before the results were announced.
The election commission said it fired four election workers in northern Balkh province for attempted fraud. Photographs showed three trying to vote with multiple cards, while the fourth was ordering voters to cast ballots for a specific candidate, said Daoud Ali Najafi, the commission's chief electoral officer.
The six other presidential candidates who cited fraud said in a statement that dozens of complaints filed could affect the outcome of the election "to the point that many are seriously questioning the legitimacy and credibility of the results."
"Fraud in the elections could result in increased tension and violence," the six added.
The most prominent of the six was Ashraf Ghani, a Western-educated former finance minister and World Bank official. Ghani earlier released a statement listing the complaints submitted by his campaign, including gunmen telling voters to cast ballots for Abdullah and officials stuffing ballot boxes in favor of Karzai.
As of Monday evening, the independent Electoral Complaints Commission said it received more than 50 allegations of fraud that could affect the election results if true. Final results cannot be certified as legitimate until the complaints commission rules on these cases.
Afghan officials say they are confident that algorithms, double-blind computer entries and other modern methods will catch 90 percent of the fraud
Associated Press Writers Heidi Vogt, Nahal Toosi, Rahim Faiez and Amir Shah in Kabul and Noor Khan in Kandahar contributed to this report.