The United Nations had called on candidates to give officials time to conduct the count and investigate fraud allegations, but Abdullah launched a verbal assault on the Independent Election Commission (IEC) one day after the vote.
He said that the turnout figure of 7 million voters announced by the IEC commissioner Ahmad Yousuf Nuristani was probably false.
And he demanded the sacking of Zia-ul-Haq Amarkhail, chief of the IEC secretariat, over an alleged attempt by Amarkhail to remove unused ballots from the IEC's headquarters in Kabul on polling day.
"There is no collaborating evidence (of the turnout figure) at all throughout the country -- that is something that is questionable and what we are concerned about is once again engineered fraud," Abdullah told reporters.
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"The head of the secretariat was... Caught red-handed and we want an investigation. We want him to be removed from his position."
Abdullah feels massive fraud denied him victory in the 2009 election, and he has often said that only a repeat of ballot-rigging could deny him power this election.
"But the candidates and their supporters should refrain from premature judgements and from criticism that is not supported with clear evidence."
Before the vote, the UN had also issued a plea for candidates to allow election officials to investigate fraud before making unproven allegations.