During a hearing of the House of Representatives' Armed Services Committee on Wednesday, Rumsfeld declined to publicly answer lawmakers who asked him the numerical strength of those fighting US troops in Iraq.
"The intelligence community looks at that. The CIA does, the Defence Intelligence Agency (DIA), others do. And they have differing assessments," Rumsfeld said.
"My job in the government is not to be the principle intelligence officer and try to rationalise differences between Iraqis, the CIA and the DIA. I see these reports. Frankly, I don't have a lot of confidence in any of them, on that number," he said.
"I am not going to give you a number for it, because it's not my business," the defence secretary said. He added he could not reveal CIA and DIA estimates because they were classified.
The Pentagon has struggled to come to grips with the size, composition and organisation of those fighting US-led troops in Iraq.
Also at the hearing, General Richard Myers, chairman of the Joint Chiefs of Staff, disputed an estimate on the number of fighters offered recently by General Muhammad Abd Allah Shahwani, director of Iraqi intelligence.
Shahwani had said there were 200,000 fighters, of whom 40,000 were hardcore.
Myers said US intelligence estimates were "considerably lower" and Rumsfeld called Shahwani's numbers "totally inconsistent" with US estimates.
Myers also admitted getting an accurate count was difficult.