He earlier told the authorities they had until Saturday to dismiss Azizullah Ludin, the head of the Independent Election Commission (IEC), although he did not say what he would do if that demand was not met.
Lodin has denied allegations of bias in favor of Karzai, and the election commission's spokesman has already said Lodin cannot be replaced by either side.
Afghanistan's runoff vote was triggered after the UN-backed Election Complaints Commission (ECC) demanded thousands of fraudulent ballots be disregarded.
Soon afterwards it was revealed that Karzai no longer had enough votes to avoid a runoff with Abdullah.
The Taliban, who threatened voters during the August balloting, have warned Afghans that they risk further attacks if they do not stay away from the polls next week.
Amid Afghanistan's election confusion, Barack Obama, the US president, has yet to make a decision on whether to send more troops to back-up US and other forces in the country.
The president reviewed his options with the joint chiefs of staff - which includes the service chiefs from the army, navy, air force and marines - in Washington on Friday, Obama's seventh such meeting.
The president's much-anticipated review of how to approach the his country's war effort in Afghanistan remains weeks away from being wrapped up.
General Stanley McChrystal, the leader of US and Nato forces in Afghanistan, has request 40,000 more troops, warning of the deteriorating situation in Afghanistan.
But the joint chiefs of staff did not make recommendations to Obama about troop levels, an unnamed senior administration official was quoted by the Associated Press as saying.
Meanwhile, the UN has demanded an explanation from Afghan and Nato officials for their slow response to a Taliban attack on a guest house in Kabul where UN staff were staying.
The UN demanded to know why it took Nato forces and Afghan police an hour to respond to the attack, which left 11 people dead, including the three attackers.
Two UN security officers battled the three fighters, who attacked the guest house at dawn on Wednesday, carrying grenades and automatic weapons and wearing suicide vests, during a two-hour siege.
Afghan authorities denied that they were slow to respond, and a Nato spokesman said the Afghans did not ask for support.