In the Taliban's former southern powerbase Kandahar, a massive bomb killed 36 people and wounded dozens more late Tuesday.
"So far we have 36 killed and 64 wounded and they are all civilians," said General Ghulam Ali Wahdad, police commander for southern Afghanistan.
There was no immediate claim of responsibility but an interior ministry spokesman blamed the attack on Taliban-linked insurgents, who have struck repeatedly during campaigning for last week's vote.
Out of the half-million ballots initially counted, the Western-backed Karzai had 212,927 votes or 40.6 percent, and former foreign minister Abdullah was on 202,889 votes or 38.6 percent, the Independent Election Commission (IEC) said.
Karzai's camp earlier insisted it had triumphed in Thursday's election, a pivotal moment in Afghanistan's troubled emergence from years of civil war and Taliban rule as Western troops battle to defeat a raging insurgency.
But Daud Najafi, the IEC's chief electoral officer, stressed that it was too early to tell with final results not due until September 3.
"I repeat again, this is partial results of about 10 percent of the overall vote," he told a news conference.
"I repeat again, this will definitely change tomorrow, the day after tomorrow. This is only partial results," the official said.
The results of Afghanistan's elections could deepen the divides that plague the shaky nation. Abdullah has his powerbase in the north, among ethnic Tajiks, while Karzai is influential in the Pashtun-dominated south.
Abdullah, the urbane former minister whose energetic campaign stymied Karzai's hopes of an easy re-election, again accused the president of rampant vote fraud but damped down fears of violence linked to a disputed outcome.
"I'm urging the Afghans to be calm and to be patient and to show responsibility," he told reporters at his home in Kabul.
"I think that the people don't want to resort to violence," he said.
"All our efforts were in order to bring stability to this country, and to bring greater governance and greater rule of law."
The United States called on Afghans to refrain from speculation and voiced hope for a transparent process to assess the fraud allegations.
"We call on all parties to refrain from speculation until the national results are announced," State Department spokesman Ian Kelly told reporters in Washington.
The IEC is releasing results piecemeal and officials have urged people not to try to extrapolate a clear picture overall. Both Karzai and Abdullah have claimed to be ahead since Thursday's vote.
"We are the winner, definitely," Din Mohammad, Karzai's chief electoral campaign official, told AFP earlier Tuesday, ruling out speculation that the president would be forced into a run-off.
Figures from Karzai's campaign office, seen by AFP and based on 95 percent of votes, show the president on track to win between 55 and 62 percent of the vote, which would save him from a potentially divisive run-off.
The figures, broken down by province and minus 480,000 votes still to be counted at IEC headquarters in Kabul, give Karzai 3,427,327, against Abdullah's 1,120,243 votes.
The figures, which indicated turnout of around 30 percent, have not been independently verified.
Karzai, whose tenure since the 2001 US-led ouster of the Taliban regime has been marred by war and corruption, won the first presidential election in 2004 with 55.4 percent of the vote.
A final result from this election cannot be certified until officials complete investigations into hundreds of alleged abuses.
Abdullah said "millions" of extra voting cards had been issued because of failures within the election commission, which stands accused of pro-Karzai bias.
"We will pursue all legal means... in order to prevent a big fraud deciding the result of our elections," Abdullah added.
Ahmad Muslim Khuram, an official with the Election Complaints Commission, said 790 complaints had been lodged relating to election day, with more than 70 of them considered significant.
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