Rumsfeld said U.S. criticism could lead terrorist sympathizers to conclude the United States will give in. He said that idea could prompt more fund raising and recruiting for terrorist groups.
"But that doesn't mean there shouldn't be a debate," Rumsfeld said. "We can live with a healthy debate as long as it is as elevated as possible and as civil as possible."
Rumsfeld also said he did not receive any new details on what has been found in the search for weapons of mass destruction in Iraq.
In other developments:
Speaking at a news conference, Annan said the United Nations would be prepared to play the key political role in helping to restore sovereignty in Iraq based on its extensive experience in establishing new governments in Afghanistan, Kosovo and East Timor after serious conflicts.
The United States proposed a draft resolution aimed at getting more peacekeeping troops and money into Iraq, but it faces strong opposition from France and Germany who are demanding speedy restoration of Iraq's sovereignty and a larger role for the United Nations. U.S. Secretary of State Colin Powell has said Washington will consider revising the resolution.
After a meeting with Iraq's new Public Works Minister Nesreen Berwari, a Kurdish woman, top American official L. Paul Bremer promised the United States would not leave Iraq before its mission was complete. He pointed to the president's massive budget request.
"This is one of the largest nonmilitary budgets requested in American history," Bremer said. "It amounts to more than 10 times more than the United States has ever spent in a year in any country.
"And it's a clear, dramatic illustration of the fact that the American people are going to finish the job we started when we liberated Iraq some four months ago," the 61-year-old former counterterrorism expert said.
Rumsfeld told reporters traveling with him that false reports in Arab news media and criticism from Democratic lawmakers in the United States complicate the terror fight.
"If you have Al-Jazeera day after day after day pounding the people of the region with things that are not true, that makes it difficult," Rumsfeld said.
Domestic criticism also hurts, Rumsfeld said.
Democrats were critical Monday of the president's massive funding request. Sen. Carl Levin of Michigan said Mr. Bush had failed to detail "an exit strategy."
Terrorists have studied the examples where attacks prompted a U.S. withdrawal from battle, such as Somalia and Lebanon, Rumsfeld said.
"They studied instances where the United States was dealt a blow and tucked in," Rumsfeld said. "They persuaded themselves they could in fact cause us to acquiesce in whatever it is they wanted to do."
Some of the strongest criticism of the war in Iraq has focused on the fact that no weapons of mass destruction have been found. Before the war, Mr. Bush said one main reason for attacking Iraq was that Saddam had chemical and biological weapons he could pass to terrorists.
Rumsfeld said Monday he is not keeping track of the hunt for weapons of mass destruction in Iraq. He called the search an issue for the CIA and other intelligence agencies.
"It's an intelligence issue," Rumsfeld said. "I made a conscious decision that I don't need to stay current every 15 minutes in that area."
Rumsfeld met in Baghdad on Saturday with David Kay, the former U.N. weapons inspector leading the American weapons hunt. Rumsfeld said the two discussed logistics, not Kay's findings.
Former weapons inspectors now say that the "unaccountable" portions of Iraq's alleged weapons of mass destruction programs may have been no more than paperwork glitches left behind when Iraq destroyed banned chemical and biological weapons years ago.
U.N. inspectors found Iraq's nuclear program in disarray and unlikely to be able to support an active effort to build atomic weapons, the nuclear agency chief said Monday.
Meanwhile, U.S. allies were reacting cautiously to the president's call for more foreign help. Japan, normally a quick backer of Washington, offered only a lukewarm response and other nations said they would like to see greater United Nations involvement in post-war Iraq first.