Election workers count provincial votes at a school, a day after Afghanistan's presidential election, in Kabul August 21, 2009.
"Initial results show that the president has got a majority," Karzai's campaign manager Deen Mohammad told Reuters. "We will not get to a second round. We have got a majority."
Abdullah, Karzai's former foreign minister, dismissed the Karzai camp's victory claim and said he was on track to win in the first round after Thursday's vote, which went ahead despite sporadic violence after the Taliban threatened the vote.
"I'm ahead. Initial results from the provinces show that I have more than 50 percent of the vote," Abdullah told Reuters by telephone in Kabul.
Official preliminary results are not due for two weeks, but counting began immediately after polls closed on Thursday and is largely complete.
Analysts have warned that uncertainty over the outcome or accusations of widespread fraud could lead to civil unrest. U.S. envoy Richard Holbrooke said he was certain the outcome of the vote would be disputed.
"We always knew it would be a disputed election. I would not be surprised if you see candidates claiming victory and fraud in the next few days," Holbrooke said at a briefing in Kabul with election observers.
Holbrooke said he Washington had an "agnostic" position and did not support any early, unofficial victory declarations.
A U.S. embassy spokeswoman said only the Independent Election Commission (IEC) was in a position to announce results and anything else was "just speculation."
Polls conducted before the election showed Karzai in the lead but suggested he would not win more than 50 percent of the vote needed to avoid a run-off.
The Karzai campaign's estimate of victory was based on reports from nearly 29,000 monitors the campaign had at polling stations throughout the country, Mohammad said.
Afghan officials and their U.S. protectors have breathed a sigh of relief after the relatively peaceful election.
PATIENCE URGED
The 6,200 polling stations are required to make their results available to the public as they tabulate them to prevent fraud.
Zekria Barakzai, deputy head of the IEC, urged patience.
"We cannot confirm any claims by campaigning managers. It's the job of the election commission to declare the results. They should be patient," Barakzai said.
Dawood Ali Najafi, another IEC official, said it was too early to say whether there would be a run-off because not all results had been received from Afghanistan's 34 provinces.
An independent Afghan monitoring body, FEFA, said it was concerned about the quality of the poll after receiving reports from its observers across the country of fraud and interference.
Barakzai said two convoys of election workers transporting ballot boxes had been attacked following the vote. In one case, in Balkh province in the north, an election worker was killed and ballots that had already been counted were burned.
He said preliminary figures showed overall turnout was around 40-50 percent. This would be roughly in line with estimates by Western diplomats before the poll.
Much is likely to depend on turnout in southern areas, such as Karzai's home province of Kandahar, where the president draws his strongest support but where voters faced the brunt of Taliban attacks and intimidation.
Abdullah's spokesman, Fazl Sangcharaki, said the north had voted solidly for Abdullah, except in Jowzjan province, home of Uzbek militia chieftain Abdul Rashid Dostum, who returned to the country days before the vote to campaign for Karzai.
Western backers have expressed concern about Karzai's tactic of seeking support from former militia chiefs, afraid that deals made to secure votes could bring warlords back to power.
In Washington, President Barack Obama hailed the conduct of the election and vowed to press on with his strategy, which has involved sending thousands of additional troops to the country.
"We have to focus on finishing the job in Afghanistan but it is going to take some time," Obama said from the White House.
The election was a test for Obama's new strategy aimed at reversing Taliban gains. U.S. combat casualties have risen amid a U.S. troop buildup and opinion polls have shown weakening American backing for the war.
(Writing by Paul Tait; Editing by Alex Richardson)
