Kerry traveled to Afghanistan from China, where he participated in the sixth round of the U.S.-China Strategic and Economic Dialogue in Beijing.
The Independent Election Commission is tallying the votes from the June 14 run-off. On Monday, the IEC announced preliminary results showing that Ghani captured 56.44 percent of the votes, with Abdullah trailing behind with 43.56 percent.
Abdullah has challenged the legitimacy of the election, alleging fraud and questioning the IEC's preliminary election results.
The White House expressed concern Tuesday that Abdullah would resort to "extra-constitutional measures" in light of the preliminary election results. The State Department similarly said it viewed "suggestions of a 'parallel government' with the gravest concern."
At a rally for Abdullah on Tuesday, supporters urged him to "Announce your government." So far, the former foreign minister has not announced a parallel government.
Kerry, the State Department said, "will discuss the ongoing political transition, reinforcing the president's message that we expect a thorough review of all reasonable allegations of fraud and that we will not accept any extra-constitutional measures."
Final election results are expected to be announced July 22.