Cheney suggested Clarke "may have had a grudge to bear," that he had left the White House after being passed over for a promotion.
It was the latest in what became a three-day cycle of broadsides, driven by Clarke's interview on CBS News' 60 Minutes in which he said Mr. Bushterrorist network while plotting to attack Iraq.
Clarke's claims are contained in a new book that is scathingly critical of administration actions. The book is published by Free Press, a subsidiary of Simon & Schuster. Both CBSNews.com and Simon & Schuster are units of Viacom.
On the eve of public hearings by the federal panel reviewing the Sept. 11, 2001, terror attacks, Cheney and other top administration officials sought to counter Clarke's accusations.
Cheney, in a telephone interview with radio commentator Rush Limbaugh, said Clarke "clearly missed a lot of what was going on" during the two years he worked at the Bush White House.
"We were all very aware of the al Qaeda threat. What I asked Richard Clarke to do was develop ideas that we could use to push forward the strategies against al Qaeda," Rice told the CBS News Early Show.
Rice said Clarke's response was a list of ideas that had been around for several years.
"The president needed more," Rice said. "He needed a strategy for al Qaeda that was going to eliminate al Qaeda."
And the president's press secretary, Scott McClellan, told a White House briefing: "His assertion that there was something we could have done to prevent the Sept. 11th attacks from happening is deeply irresponsible. It's offensive and it's flat-out false."
The ferocity of the White House response has everything to do with the coming election, in which the President has made his leadership in taking the fight to Afghanistan and Iraq an applause line at every stop, reports CBS News Correspondent Bill Plante.
White House officials
Clarke resigned his White House job 13 months ago, after holding senior posts under Presidents Reagan and Clinton and the first President Bush.
In his book, "Against All Enemies," Clarke wrote that the current president "launched an unnecessary and costly war in Iraq that strengthened the fundamentalist, radical Islamic terrorist movement worldwide."
Clarke told 60 minutes that immediately after the attacks on Sept. 11, the administration
"Well, (Defense Secretary Donald) Rumsfeld was saying that we needed to bomb Iraq. And — and we all said, 'But no, no. Al Qaeda is in Afghanistan. We need to bomb Afghanistan.' And Rumsfeld said, "There aren't any good targets in Afghanistan and there are lots of good targets in Iraq."
Clarke says he told the president there was no connection between Iraq and al Qaeda, but that apparently wasn't what Mr. Bush wanted to hear.
"He came back at me and said 'Iraq. Saddam. Find out if there's a connection.' And in a very intimidating way — I mean, that we should come back with that answer," Clarke said.
Clarke's claims echoed those of another former administration official, one-time treasury Secretary Paul O'Neill, who claimed Mr. Bush's first national security council meeting.
Cheney said of Clarke's assertions, "I fundamentally disagree with his assessment both of recent history, but also in terms of how to deal with the problem" of global terrorism.
The White House took issue with a conversation Clarke reported he and several other aides had with Bush in the White House Situation Room on Sept. 12, 2001, the day after the terror attacks.
"See if Saddam did this," Bush is quoted by Clarke as saying.
McClellan said Bush "doesn't have any recollection" of such a meeting or conversation.
Furthermore, McClellan said, "there's no record of the president being in the Situation Room on that day that ... you know, when the president is in the Situation Room, we keep track of that."
At the Pentagon, Defense Secretary Donald H. Rumsfeld told reporters that the administration had discussed early military action against Iraq, but not in the context of the Sept. 11 attacks. It was instead focused on the fact that Iraqi air defenses were targeting U.S. and British fighter aircraft enforcing no-fly zones over northern and southern Iraq.
"That was the one place on the face of the earth where a country — in this case Iraq — was firing at aircrews of the United States and the United Kingdom that were enforcing U.N. resolutions. There is no question but that there was discussion about Iraq, and it was in that context," Rumsfeld said.
McClellan and Rice portrayed Clarke as having left the White House after being passed over to be deputy of the new Department of Homeland Security. They also said he boycotted regular meetings held by Rice, and they cited his friendship with Rand Beers, a national security adviser to Democratic presidential candidate John Kerry.
"It's important to keep in context we're in the heat of a presidential campaign and all of a sudden he comes out with a book that he is seeking to promote ... and he is making charges that simply did not happen," McClellan said.
"This is Dick Clarke's American grandstand. He just keeps changing the tune," McClellan added.
Clarke is scheduled to testify, along with Defense Secretary Donald Rumsfeld, Secretary of State Colin Powell, CIA Director George Tenet and top national security officials from the Clinton administration. Rice was invited but declined.
McClellan noted that Rice had privately met with the commission for four hours.
Seven Democratic senators, meanwhile, wrote to Bush protesting the decision not to allow her to testify, saying her refusal "can only lead the American people to one conclusion: that she has something to hide and is not fully committed to finding the truth."
Signing the letter were Sens. Robert Byrd of West Virginia, Jon Corzine of New Jersey, Hillary Clinton of New York, Christopher Dodd of Connecticut, Edward M. Kennedy of Massachusetts, Frank Lautenberg of New Jersey and Charles Schumer of New York.
Bush and Cheney have agreed to private, separate meetings with the commission's chairman and vice chairman. McClellan said there has been no decision on scheduling.