Taliban offensive
The US has been concerned at reports that Mr Abdullah, who preliminary results suggest lost the election, is planning a "parallel government".
Results announced by Afghanistan's election officials give Mr Ghani 56.44% of votes in the 14 June run-off, with Mr Abdullah gaining 43.45%.
The results were markedly different from those achieved in the first round of voting, held in April.
In that round, Mr Abdullah fell just short of an outright majority, with 44.9%, with Mr Ghani second at 31.5%.
Votes are already being re-checked at more than 7,000 polling stations - nearly a third of the total number.
Correspondents say recounts could significantly alter the final result, due on 22 July.
The UN Assistance Mission to Afghanistan has warned it will be "premature" for either side to claim victory.