Abdullah also called for the suspension of three cabinet ministers on Monday as he laid out a raft of conditions ahead of the runoff.
He gave the authorities time until Saturday to sack Azizullah Ludin, but refused to say what he would do if Ludin, a former presidential advisor, and the ministers stayed in place.
Concerns about a repeat of the fraud have cast a shadow over preparations for the runoff.
More than 200 election officials are being fired or replaced to prevent that.
One of Abdullah's closest supporters said there was a strong likelihood that the former foreign minister would boycott the November 7 runoff.
"Unless these conditions are met, holding a transparent, just and free election is not possible," Ahmad Behzad, a parliamentarian who campaigned for Abdullah in the first round of the presidential poll, said.
"If the conditions are not met, there is a big possibility of a boycott by Dr Abdullah."
"Another commissioner from the same commission should take his position."
The United Nations-backed Electoral Complaints Committee discarded around a quarter of the votes from the August 20 poll because of fraud.
Some polling stations reported more than 100 per cent turnout while others saw ballots hugely favouring one candidate.
Ban Ki-moon, the UN secretary-general, has said that around 200 IEC field officers will be replaced for the second round.