There was no immediate reaction from Abdullah's camp on Karzai's call.
Meanwhile, Azizullah Ludin, the chairman of Afghanistan's election commission, has stressed that election would be held despite Abdullah's withdrawal.
"Under the law there is no alternative but to have these elections," Bays quoted him as saying.
Bays said that holding the election with one candidate would pose a "vast organisational headache" and "security headache" although people will be turning out to vote for just one candidate.
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.
Al Jazeera's James Bays on the one-man race that is the Afghan presidential runoff vote
The discovered fraud pushed Karzai below the required 50 per cent margin needed to win, forcing the country into a second round.
Abdullah had demanded that Karzai sack Ludin and suspend four ministers who campaigned for the president.
He told supporters on Sunday a "transparent election is not possible" and that the Afghan government has been illegitimate since May.
"I'll not take part in the election," Abdullah said, adding that he had "not taken this decision easily".
In an interview with Al Jazeera shortly after the announcement, he said the decision was made after "a lot of consultations".
"It was the right decision, and I did it in the best interests of this country," Abdullah said.
Abdullah said that as far as the process is concerned, "hopefully there is a way forward".
"I will not enter into the constitutional implications of this decision," he said.
"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."
The US, at the forefront of a miltary campaign to fight the Taliban in Afghanistan, has said it is ready to work with the next Afghan president despite questions about the government's legitimacy.
Valerie Jarrett, a senior adviser to Barack Obama, the US president, said Abdullah's announcement should not further delay the White House's strategy review on Afghanistan that has already dragged out for months.
"We're going to work with the leader of the Afghan government, and hopefully that's going to create the state of conditions for the people of Afghanistan, and also help us as we try to bring this war to a close," she said on a US talk show.
David Axelrod, another senior Obama adviser, said "obviously there are issues we need to discuss, such as reducing the high level of corruption" in Afghanistan, but he said "we are going to deal with the government that is there".
Obama and his national security advisers have been reviewing the US role in the eight-year war in Afghanistan, where 68,000 American troops will be fighting by the end of the year.