CNN said on its website on Friday that Jordan conceded his remarks at last month's World Economic Forum in Davos were "not as clear as they should have been".
Several participants at the event said Jordan told the audience US forces had deliberately targeted journalists - a charge he denied.
Jordan quickly explained that some journalists were killed because they were in the wrong place at the wrong time, and were struck by a bomb, while others died because American forces mistook them for the enemy.
But his comments erupted into a controversy that he said threatened to tarnish the network he helped build, according to CNN.
"I have decided to resign in an effort to prevent CNN from being unfairly tarnished by the controversy"
CNN chief news executive
"After 23 years at CNN, I have decided to resign in an effort to prevent CNN from being unfairly tarnished by the controversy over conflicting accounts of my recent remarks regarding the alarming number of journalists killed in Iraq," Jordan said in a letter to colleagues.
Speaking to Aljazeera from New York, Dr Fawaaz Jajis, a professor of political science at University of Lawrence, said there is little room for voices of dissent in America.
"The United States is in a state of war, militarily and ideologically," Jajis said.
'Casualty of war'
"Unfortunately, it seems that the truth is one of war's victims, as is freedom of the media, journalism and opinion in the United States," he added.
The controversy gained steam last week, with internet bloggers posting their accounts of what transpired at the Switzerland forum, an event attended by political, economic, academic and media figures from around the world, the CNN site said.
The Davos organisers have said the session, like most at the forum, was off-the-record, and they have declined to release a transcript to preserve their commitment.
The resignation sent shock waves through CNN, the network said, because Jordan has been long admired by his colleagues, from executives to the rank-and-file.
Jordan joined CNN as an assistant assignment editor in 1982 and rose through the ranks to become CNN's chief news executive.