The June 14 election triggered a tense standoff between Abdullah and his poll rival Ashraf Ghani, with both candidates claiming victory amid allegations of massive fraud.
To end the impasse, a deal was brokered for an audit of all eight million votes to remove fraudulent ballots, and for the formation of a national unity government under whoever becomes the next president.
But with the audit entering its final stages, Abdullah's campaign team ignored pleas from the United Nations and the United States to allow the process to finish and then to respect the final outcome.
"Such a process is not acceptable for us and has no value."
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He said Abdullah's demands over how fraudulent votes should be thrown out had been ignored.
Abdullah won the eight-candidate first-round election in April, but preliminary results in the June run-off vote showed he had fallen well behind Ghani.
Yesterday the invalidation stage of the audit finally began - but Manawi dismissed it as "a joke".
The country has been in paralysis for months due to the election to choose the successor to President Hamid Karzai, who will step down as US-led NATO troops prepare to end their 13-year war against Taliban insurgents.