Clarke's exclusive interview will be broadcast on 60 Minutes, Sunday, March 21 at 7 p.m. ET/PT.
Clarke was surprised that the attention of administration officials was turning toward Iraq when he expected the focus to be on al Qaeda and Osama bin Laden.
"They were talking about Iraq on 9/11. They were talking about it on 9/12," says Clarke.
The top counter-terrorism advisor, Clarke was briefing the highest government officials, including President Bush and Secretary of Defense Donald Rumsfeld, in the aftermath of the September 11 attacks.
"Rumsfeld was saying we needed to bomb Iraq....We all said, 'but no, no. Al Qaeda is in Afghanistan," recounts Clarke, "and Rumsfeld said, 'There aren't any good targets in Afghanistan and there are lots of good targets in Iraq.' I said, 'Well, there are lots of good targets in lots of places, but Iraq had nothing to do with [the September 11 attacks].'"
Clarke goes on to explain what he believes was the reason for the focus on Iraq.
"I think they wanted to believe that there was a connection [between Iraq and al Qaeda], but the CIA was sitting there, the FBI was sitting there, I was sitting there, saying, 'We've looked at this issue for years. For years we've looked and there's just no connection,'" says Clarke.
Clarke also tells Stahl that the president isn't doing the best job fighting terrorism.
"Frankly, I find it outrageous that the president is running for re-election on the grounds that he's done such great things about terrorism," says Clarke in Sunday's interview. "He ignored it. He ignored terrorism for months, when maybe we could have done something to stop 9/11. Maybe. We'll never know."
Clarke, who advised four presidents, reveals more about the current administration's reaction to terrorism in his new book, "Against All Enemies," published by Free Press, a subsidiary of Simon & Schuster. Both CBSNews.com and Simon & Schuster are units of Viacom.