In front of a live-televised news conference on Wednesday, Abdullah announced that his campaign had decided to suspend "engagement with the (election) commission," and that there was "no way the counting could continue in the absence of (his campaign's) monitors."
Abdullah also took to Twitter to express his concern about election fraud.
"Counting process should be stopped because this process is not transparent at all. I declare this as a candidate for Afghanistan's presidential election."
"It is the right of the people to defend their vote. Fraud is taking place in every corner of the country and hurting the Afghan people."
The Independent Election Commission responded, saying that the vote count would continue and that it was too early to determine whether the count was successful or not. IEC spokesman Noor Mohammed Noor requested complaints be withheld until after a winner is announced.
Election results are expected July 22.
Abdullah, a former foreign minister, secured 45 percent of the April 5 vote while his contender, former Finance Minister Ashraf Ghani, got 31.6 percent of the votes. Because neither candidate obtained more than the required 50 percent of the vote to win a first-round election, the runoff was held on Saturday.
Abdullah Abdullah voiced similar allegations of election fraud when he ran in -- and dropped out of -- the 2009 election.
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