The eventual winner will have to oversee the fight against a resilient Taliban insurgency as 51,000 US-led NATO combat troops leave Afghanistan this year.
Five NATO soldiers died on Saturday in a helicopter crash in the south of the country, officials said, adding that the cause of the incident was being investigated.
Karzai, who is constitutionally barred from serving a third term, has pledged to stay neutral in the election.
But he was widely thought to have backed former foreign minister Zalmai Rassoul, who took just 11 percent of the vote on the partial count.
Rassoul could still play a key role in power-brokering before the next president is chosen, as could former Islamist warlord Abdul Rab Rasoul Sayyaf, who collected a significant seven percent of the vote on the partial count.
All leading candidates have pledged to explore peace talks with the Taliban and sign a deal with the US that could allow 10,000 US troops to stay on after this year on a training and counter-terrorism mission.
Karzai’s surprise decision to refuse to sign the bilateral security agreement last year after agreeing to the draft text plunged relations between Afghanistan and its biggest donor to a new low.
The outgoing president has had several public disagreements with Washington in recent years, underlining efforts to establish his reputation as an independent, nationalist leader despite relying on US aid and military power during his reign.
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