Ludin and Daoud Ali Najafi, his number two, had previously tendered their resignations although they had not been accepted, Omer said.
Pressure has been high on Karzai to ensure that parliamentary elections, to be held in September, are fair.
In last year's presidential vote, which the IEC oversaw, a third of the votes for Karzai were declared invalid following a probe by a UN-backed watchdog, the Election Complaints Commission.
Al Jazeera's James Bays, reporting from Afghanistan's Helmand province, said: "Ever since that election, one of the key demands of the international community behind closed doors to President Karzai has been the removal of these two [IEC] men.
"But it's not all over yet because we don't know who Hamid Karzai is going to put in these two jobs.
"There's a lot of talk in Kabul right now concerning one man, he's called Abdul Karim Khurram. He's a Karzai loyalist, one of his closest supporters ... and word in Kabul at the moment is that he might get the job as the chairman of the Independent Election Commission."
Last week, Karzai admitted that there had been widespread fraud but angered the international community by claiming that foreign governments were to blame.
"There was fraud in presidential and provincial council elections - no doubt that there was a very widespread fraud, very widespread," Karzai said.
"But Afghans did not do this fraud. The foreigners did this fraud."
The United States called the comments "troubling" and hinted that Karzai's invitation to visit Washington for talks with Barack Obama, the president, could be withdrawn.
But Karzai's spokesman later said the president's remarks would not affect strategic relations between his government and the international community.
"It [Karzai's remarks] did not have any effect on the strategic relations with the United States and the international community," Omer said on Wednesday.
"The strategic relationship between Kabul and Washington is still in the partnership of the international community. Our stance and position are the same," he said.