Ramazan Bashardost, a popular Kabul lawmaker, scored 108,156 and Ashraf Ghani , a former World Bank economist, took 27,697 votes, Najafi said.
James Bays, Al Jazeera's correspondent in Kabul, said: "Twenty-four hours ago we had just 10 per cent. We have a bit of a better picture now. Dr Abdullah has lost his position a little.
"We are going to get more results in coming days. They say they are going to take a break to collate more, so they will have more results for us on Saturday. That could be more than 50 per cent of the vote collated."
Final, certified results will not be made public until mid or late September, after investigations are held into the dozens of complaints of serious fraud that have been filed.
Low voter turnout and allegations of fraud have cast a pall over the election.
Abdullah has accused Karzai of rigging, including ballot-stuffing and voter intimidation. Karzai's camp denies the accusations.
The Electoral Complaints Commission, backed by the UN, said on Tuesday that it had received 790 complaints since election day.
Fifty-four of those cases were given "high priority" and were considered serious enough to potentially affect the result, the group said.
The complaints had more than tripled since Sunday when 225 objections had been registered.
Karzai needs a simple majority of more than 50 per cent to avoid a second round run-off. Otherwise, a run-off is planned at the beginning of October.