Asked if US forces had samples of Saddam's DNA, he said: "Oh, of course _ what you should know is that we have the forensic capability to chase these things down and we'll chase them down, every one of them, all the way."
"The appropriate people with the appropriate forensics are doing checks _ in each of the places where we think we may have killed regime leadership."
Identifying Saddam as dead or catching him alive is crucial both to Washington's claim to victory and to assuring the Iraqi people that they are free of the dictator and can express themselves freely.
Gen Franks also said coalition forces had DNA samples from other leaders in the Iraqi regime.
Until recently the only rumoured sample of Saddam's DNA in American possession was supposed to have been provided to the Americans by an estranged mistress and taken from a razor blade or teacup.
Experts believed such a source would be useless unless it could be conclusively determined that the objects were only used by Saddam.
The other hope was that they might be able to use DNA from close relatives of the dictator to increase the probability of making a correct identification.
The children of one of Saddam's half-brothers are believed to be in Switzerland.
And three of Saddam's daughters, Raghad, Rana and Hala, are thought to be still alive.
With genetic material from a son or daughter, a DNA sample could be shown with 90% certainty to have come from Saddam, said Mark Stolorow, executive director of Orchid Cellmark, a Maryland company that conducted DNA testing on victims of the September 11 attacks.