Afghan presidential candidate Ashraf Ghani has called for an “extensive audit” of votes.
Ashraf Ghani made the appeal before meeting US Secretary of State John Kerry, who arrived in Kabul to try to resolve a growing political crisis.
John Kerry is also meeting Ashraf Ghani’s rival Abdullah Abdullah.
Ashraf Ghani came out ahead in preliminary results from the second round, but both candidates allege fraud.
The audit would help ensure the “integrity and the legitimacy that the people of Afghanistan and the world will believe in,” Ashraf Ghani said.
The announcement was welcomed by John Kerry, who arrived in Afghanistan on Friday in a hastily arranged visit.
“No one is declaring victory at this time. The results have yet to be finalized and so those questions have to be resolved and I’m very appreciative that Dr. Ghani respects that” he said.
Current President Hamid Karzai, who took power after the US-led overthrow of the Taliban, is stepping down after more than 10 years.
The US has been concerned at reports that Abdullah Abdullah, who preliminary results suggest lost the election, is planning a “parallel government”.
Results announced by Afghanistan’s election officials give Ashraf Ghani 56.44% of votes in the June 14 run-off, with Abdullah Abdullah gaining 43.45%.
The results were markedly different from those achieved in the first round of voting, held in April.
In that round, Abdullah Abdullah fell just short of an outright majority, with 44.9%, with Ashraf 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 July 22.
The UN Assistance Mission to Afghanistan has warned it will be “premature” for either side to claim victory.
There are also concerns about a further deterioration in the security situation.
Taliban militants have been testing the limits of the Afghan army in recent weeks, with a major offensive in the southern province of Helmand.
The withdrawal of foreign troops by the end of this year will be the litmus test of whether more than a decade of training and investment in building up Afghanistan’s own security forces has paid off, correspondents say.
President Barack Obama has said the US remained committed to Afghanistan provided the incoming president signed a security agreement.
Both Abdullah Abdullah and Ashraf Ghani have said they are committed to signing the deal with the US that would allow a small force to stay on.
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