According to the Independent Election Commission, Ghani has so far captured 56.44 percent of the votes in the June 14 run-off. His competitor, former Foreign Minister Abdullah Abdullah has 43.56 percent of the votes so far tallied.
Abdullah, who last month denounced the election due to concerns of election fraud, issued a statement on Monday in response to the preliminary results.
"As we had rejected the outcome of the result before and had declared that we could not trust the election commission, our stand is the same today," Abdullah's spokesman told the BBC.
Chief election commissioner Ahmad Yusuf Nuristani acknowledged there were "some mistakes in the overall process" and that the latest figures are "only initial results... There is a chance of change in the overall figure."
The final election results are expected July 22.