Speaking at a news conference in Kabul on Wednesday, Azizullah Ludin, the IEC chairman, confirmed the next election would take place on November 7.
"The IEC has started to deploy staff and equipment around the country, beginning at the provincial capitals ... we have the necessary funds for a second round of elections", Ludin said.
"The world has expectations that there will be good elections in Afghanistan."
The chairman also said his commission would bring those who committed fraud in the last elections to justice, but warned that this would be no easy task.
"You know that during the August elections, we lost staff ... 15 of our staff were killed, and another 20 were wounded," Ludin said.
James Bays, Al Jazeera's correspondent in the Afghan capital, Kabul, reported that Abdullah had softened his combative approach towards Karzai.
"The whole tone of this news conference has been moderate," he said. "He has been very conciliatory towards Karzai.
"I think that both men have been told [by the US and international powers] to do that to try to avoid any trouble that may break out, any spontaneous trouble for example on the streets."
Bays said that Abdullah had also not openly criticised the IEC which organised the first poll.
"He's been very strong in the past saying that the chairman of that commission is a Karzai man and that he cannot be trusted.
"One of Abdullah's aides told me that he [Abdullah] is trying to get other figures in the international community - possibly the US, possibly the UN - to put pressure on the IEC to change things.
"If Abdullah comes out and says the chairman must resign, Karzai will probably stand up to that and say 'no, I back the chairman'.
"But if the UN or the international community says that they want to see changes, then there might be changes."
Grant Kippen, the chairman of the UN-backed Electoral Complaints Commission (ECC), told Al Jazeera from Kabul: "There were irregularities in the first round, but I think that the IEC is looking at how they can avoid such a repeat.
"They are looking at different measures that they could put in place."
Kippen said that he could not comment on whether those measures would include sacking the head of the IEC.
"The IEC is an independent body and they have their rules and procedures. We simply are responsible for looking at irregularities," he said.
Kippen said that it would be left to the IEC to ensure the smooth running of the next round.
While the decision to hold the runoff has been hailed in many quarters, concerns remain over how it can be organised at such short notice.
Providing security for the elections will pose a serious challenge, particularly at a time when there has been an upsurge in attacks by the Taliban and al-Qaeda.
But talking to Al Jazeera after the news conference, Abdullah said that a successful election could be held.
"There are a lot of challenges ahead of us ... but at the same time I think that it is possible," he said.
"The international community has assured us that they are well prepared to help us. Once again, they deserve our thanks."
Prior to the announcement of a second round, there had been intense speculation that Karzai and Abdullah would reach a power-sharing deal.
According to sources, there were detailed talks between the two camps and discussions about who was going to get which ministry.
Those talks apparently broke down without reaching an agreement.
Abdullah's agreement to take part in a runoff election comes as Barack Obama, the US president, considers whether to send thousands more US troops to Afghanistan to combat fighters loyal to the Taliban and al-Qaeda.
General Stanley McChrystal, the commander of US and Nato troops in Afghanistan, has warned that the military mission risks failure unless more soldiers are sent to the country, and is understood to be seeking up to 40,000 extra troops.
The White House has said that Obama could make a decision before the runoff.
|The US president is considering sendING thousands more troops to Afghanistan [GALLO/GETTY]
But John Kerry, a US senator and chair of the US senate foreign relations committee, said that he believes the president should make a decision after the election.
"I think it's critical to have a runoff. It's a two-week period. I think you really want to know that this has worked. And you want to know what kind of government has come out of it," he said on Wednesday.
"I would absolutely counsel the president to wait till the end of the runoff."
Ambassador Richard Haass, the president of the Council on Foreign Relations and a former policy director at the US department of state, said that there no "rush" for Obama to make a decision on military strategy.
"The situation in Afghanistan is not teetering on the edge, and even if tomorrow the [US] president decided to send more troops, it could take months to actually get them there.
"Also, the mere fact that we are considering what to do gives us some leverage vis a vis those in Kabul who are making the decision on elections.
"So, for these reasons, not only is there no need to rush the decision, we might as well wait several weeks to see how the election goes and, more importantly, how the process of government creation goes."