"It was the right decision, and I did it in the best interests of this country," Abdullah said.
"As far as the process is concerned, hopefully there is a way forward. I will not enter into the constitutional implications of this decision.
"But I'll be pursuing the agenda for change and reform in any capacity that I'll be. Perhaps, after a sigh of relief, I will enter into this role with my followers, with my supporters, with the movement that has supported me for the past five months."
Shortly after Abdullah's announcement, the campaign team of Hamid Karzai, the Afghan president, said the election would still go ahead.
"His [Abdullah's] withdrawal should not alter the process... The process should go on and the people of Afghanistan should be given the chance to vote," Wahid Omar, a Karzai spokesman, told Al Jazeera.
In Sunday's statements, Abdullah said a "transparent election is not possible" and that the Afghan government has been illegitimate since May.
The supreme court, appointed by Karzai, extended his mandate after the election was put off from last spring until August.
Earlier, Karzai had rejected a series of demands laid down by Abdullah, who previously served as foreign minister in his cabinet.
Following widespread fraud in the August first round, Abdullah had demanded that 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.
James Bays, Al Jazeera's correspondent in Kabul, said many Afghans had told him that an election with only one candidate would be "farcical".
"I've been speaking to Afghans and they're all telling me the same thing: They believe that an election with only one candidate would be simply farcical," he reported.
"One educated Afghan said to me that one of the great things that the West has always boasted about after the days of the Taliban, was bringing democracy to Afghanistan. [But] many Afghans are asking what sort of democracy results in a second-round election with only one candidate."
Voter turnout crucial
Haroun Mir, a political analyst in Kabul, said that the credibility of the election would depend on turnout.
"Everything will depend on the voter turnout," he told Al Jazeera.
"If the turnout is high, as in the first round, Karzai will be declared winner and he'll have legitimacy in the eyes of the Afghans and in the international community.
"But if the turnout is very low - below 25 per cent - Karzai will be declared legally as president, but will not enjoy strong legitimacy within the Afghan population or indeed the international community."
The first round of Afghanistan's elections on August 20 was so badly affected by ballot-box stuffing and distorted tallies that more than one million votes were thrown out.
The fraud pushed Karzai below the required 50 per cent margin needed to win, forcing the country into a second round to be held on November 7.