An electoral official on Thursday said that counting would begin within hours.
"Ballot boxes that are not being held for investigations [will] return to the normal flow of the counting process," he said, referring to an inquiry by an international panel into alleged irregularities.
The counting process was put on hold earlier in the week after several candidates in Saturday's election charged that there was fraud and irregularities.
The main complaint was that ink used to stain voters' fingers and prevent multiple voting was found to wash off.
The complaints will be investigated by the UN-Afghan Joint Electoral Management Body (JEMB) and a three-person international panel which was set up by the United Nations.
Early and partial results are expected within days but a final result could take several weeks, officials have said.
US-appointed interim President Hamid Karzai is widely expected to win the country's first direct presidential election against 17 other candidates.