Afghan law states that a candidate must win more than 50 per cent of the vote to avoid a run-off.
Officials have still not given a figure for overall election turnout.
The results will not be finalised until September, after the election watchdog has examined the allegations of fraud that have overshadowed what is only Afghanistan's second direct presidential election.
The complaints watchdog has said it is investigating more than 2,000 accusations of fraud and abuse, including 270 thought serious enough to alter the outcome.
A large number of fraud allegations have been concentrated in Afghanistan's southern provinces, which largely support Karzai.
Al Jazeera's James Bays, in Kabul, said: "There are so many complaints being lodged that the figures we have are preliminary figures.
"It's going to be a very long process."
The southern provinces have been late to report results, but they are also the areas where Taliban violence and threats were most successful in scaring away voters.
Afghanistan's election is also a test for the strategy of Barack Obama, the US president, who has order thousands of extra troops to Afghanistan in a bid to reverse Taliban gains.