The Independent Election Commission (IEC) said Abdullah was on 44.4 per cent with former World Bank economist Ghani on 33.2 per cent of the ballots so far counted from April 5, when eight candidates contested the race to succeed Hamid Karzai.
If no single candidate gains more than 50 per cent of the vote, a run-off between the two leading names is tentatively scheduled for May 28.
"Almost half of the clean votes have been counted," Ahmad Yousuf Nuristani, the IEC chief, told reporters.
With 3.45 million votes now counted, the overall turnout is set to be nearly seven million voters from an estimated electorate of 13.5 million people -- far above the 2009 turnout.
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The eventual winner will have to lead the fight against a resilient Taliban insurgency as US-led combat troops prepare to leave Afghanistan this year, and must also strengthen an economy reliant on declining aid money.
Both candidates have expressed confidence they will win the election on the first round, but have also vowed to fight on if a run-off is necessary.
Abdullah, who came second to Karzai in 2009, has signalled that he may be open to constitutional changes that could allow for a power-sharing deal before the run-off.
Ghani, a former World Bank economist, has also raised the issue, but it is uncertain how any new system could accommodate the two rivals or how long it would take to implement.