"I will not take part in the election ... I've not taken this decision easily," Abdullah told reporters in Kabul on Sunday.
He stated that a "transparent election is not possible", but meantime, stressed the he was not calling for a boycott.
Earlier on Saturday, Fazel Sancharaki, Abdullah's campaign spokesman, told FNA that if Karzai does not provide a positive response to Abdullah's conditions, then Dr. Abdullah will announce his stance in a conference on Sunday.
Abdullah, who ranked second to Karzai in the first round of voting on August 20, had demanded Karzai sack Azizullah Ludin, the head of the Independent Electoral Commission (IEC).
He also demanded the suspension of four ministers who campaigned for Karzai.
Abdullah's camp had set a deadline of Saturday for Karzai to bow to his demands.
Supporters had earlier intimated Abdullah would not take part in the contest, saying it will not be free and fair.