KABUL, Afghanistan — Afghanistan will conduct an audit of the entire eight million votes cast in the recent presidential election, Secretary of State John Kerry announced Saturday, a deal he brokered to resolve a tense power struggle between the top two presidential candidates over allegations of widespread vote fraud.

The audit, which will begin immediately, will be supervised by international monitors and its results will be binding, according to the agreement announced by Mr. Kerry and endorsed by the rival candidates at a news conference in Kabul, the capital. “Every single ballot that was cast will be audited,” he said. The breakthrough came on the second day of a visit that Mr. Kerry hastily arranged to try to prevent Afghanistan’s first democratic transfer of power from collapsing. Both candidates, Abdullah Abdullah and Ashraf Ghani, had said the election was marred by fraud, but both had also claimed victory.

Tensions rose Tuesday when Mr. Abdullah threatened to form his own government, raising the possibility of an ethnically and regionally divided Afghanistan just as American troops prepare to complete their withdrawal.