More than seven million people defied Taliban threats of violence in Saturday's election to select a successor to President Hamid Karzai as US-led troops prepare to exit the country.
Unless one candidate gets more than 50 per cent of the vote, the top two names will go head-to-head in another election scheduled for late May.
Campaign officials for former World Bank economist Ashraf Ghani and for Abdullah Abdullah, who came second in the 2009 election, both said that they were well ahead in unofficial counting.
"We have to wait for the announcement made by the IEC (Independent Election Commission), but if its decision is to go to the second round, we are fully prepared for that with confidence in our ultimate success."
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Abdullah had vowed on the campaign trail to secure a first-round victory, and his team has been upbeat since the vote.
"Analysis by our database centre shows that our election ticket is in the lead, scoring 62 percent of the votes that we have counted," said Abdullah's spokesman Mujib Rahman Rahimi.