But he added that some of the information security officials were receiving may have been deliberately meant to mislead US authorities.
Senate Majority Leader Tom Daschle is pressing for an independent commission to investigate possible intelligence failures leading up to the attacks on New York and Washington.
But Vice-President Dick Cheney rejected the idea, saying that a new commission would leak intelligence secrets and undercut US efforts to prevent future attacks.
New fears
A flurry of new security warnings from several US officials has led to suggestions that President George W Bush's administration is trying to counter criticism of its role before last year's attacks.
Mr Rumsfeld said this week that he believed it was inevitable that terrorist groups would get their hands on nuclear, biological or chemical weapons.
Secretary of State Colin Powell said he believed terrorists were "trying every way they can to get their hands on weapons of mass destruction".
FBI Director Robert Mueller also warned it was "inevitable" that suicide bombers would strike the US sooner or later, and Mr Cheney has said that more terror attacks on America were "almost certain".
Landmarks protected
In New York, security has been tightened around the city's landmarks, including the Statue of Liberty and the Brooklyn Bridge, following warnings from the FBI they may be the target of attacks. But Mr Rumsfeld insisted he had not been prompted by criticism of the Bush administration, saying he hadn't changed his message for months.
But he did suggest that some of the information Washington is receiving - including possibly from those held at Guantanamo Bay, in Cuba, is meant to mislead US officials.
"These people are well trained," he said.
"My goodness, you have seen their training manuals. They know precisely what they are doing and they are taught all kinds of techniques in a whole host of different areas.
"We are certainly finding that in the interrogations in Guantanamo, that they are very well trained in interrogation techniques."
Mr Rumsfeld said giving false information could show how the United States would respond to particular situations or simply force it to waste resources.
Mr Cheney has also denied that the spate of warnings was aimed at deflecting criticism of the Bush administration.
"In this work... you're damned if you do, damned if you don't," he said.
He rejected the idea that President Bush had any forewarning of the 11 September attacks.
Mr Daschle said he wanted outside experts to collect and review possible warning signs that were missed.
But President Bush, who has come under strong criticism over FBI memos that were apparently not followed up, says the intelligence committees already at work are the best way to proceed.
"Our concern is that if we now lay another investigation on top of that (it) would just multiply the potential sources of leaks and disclosures of information that we can't disclose," Mr Cheney said.