KABUL, Afghanistan — Afghanistan’s election crisis has twisted through each of the past 10 days, as the presidential candidate Abdullah Abdullah has wielded boycott and brinkmanship in his quest to expose what he calls industrial-scale fraud against him.

On Monday, he won his first major concession, when one of the country’s top election officials resigned after repeated accusations by Mr. Abdullah that he was at the heart of a conspiracy to rig the presidential runoff.

The official, Ziaulhaq Amarkhil, said in an emotional news conference here that he was stepping down “for the sake of the country and for national unity.” But he maintained that he was innocent. And he criticized Mr. Abdullah’s release of audio recordings that the candidate has offered as evidence that Mr. Amarkhil was directing widespread ballot-box stuffing, saying the tapes had been faked.

The tapes, whose authenticity could not be verified, are a compendium of conversations between a man said to be Mr. Amarkhil and an array of subordinates, as well as people said to be campaign staff members for the other presidential candidate, Ashraf Ghani. The recordings, which the Abdullah campaign made available to reporters, include the voices of men chuckling about “stuffing the sheep,” which the Abdullah campaign says is code for stuffing ballot boxes.