Abdullah's team had blocked the IEC from accessing the recount in seven of the 34 provinces in Afghanistan, which hindered the publication of preliminary results of the September 28 polls.
"After broad consultations between the leadership of our electoral team, the leadership decided that our supporters tomorrow (Sunday) allow the commission to start its audit and recounting process of votes in all seven provinces of the country where the process was blocked by our supporters" Faridoon Khwazoon, a spokesperson for Abdullah's team, told Efe news on Saturday.
Khwazoon added that the decision was taken to show "good will" and allow IEC to reconsider their decisions regarding 300,000 disputed votes, which are considered to be invalid by Abdullah's team.
Of the 2.7 million votes cast on September 28, only 1.92 million were biometrically verified, and out of those the commission declared 86,000 null and void.
Abdullah's team said the number of invalid votes was higher than that, and put the figure at more than 300,000.
"The decision to allow the audit and recounting process in seven provinces doesn't mean that we are withdrawing from our demands regarding the 300,000 votes, we still want them to be invalidated," Khwazoon said.
He further said that until the decision on disputed votes gets resolved they will not accept either partial or preliminary results.
The preliminary results were first scheduled to be announced on 19 October but was delayed until November 14.
It was later shifted to an unspecified date due to technical problems and the blockage of the audit process by some candidates.
The audit and recounting process which was started on 10 November has already been completed in 27 provinces.
"We welcome the decision of the electoral team (of Abdullah) to remove the obstacles ahead of the audit and recounting process, we will try to start the process in these provinces tomorrow (Sunday) and complete it soon and prepare for the announcement of the results," IEC spokesperson Abdul Aziz Ibrahimi told Efe news.
( With inputs from IANS )