Rumsfeld was speaking after a trip to Afghanistan and Iraq where he sought to highlight progress on reconstruction efforts and dampen criticism of the U.S. presence there and the almost daily casualties in a guerrilla campaign against occupation.

He said if Washington's enemies believed Bush might waver or his opponents prevail, that could increase support for their activities.

"They take heart in that and that leads to more money going into these activities or that leads to more recruits or that leads to more encouragement or that leads to more staying power," he told reporters traveling with him on his plane.

"Obviously that does make our task more difficult."

"Terrorists studied...instances when the United States was dealt a blow and tucked in, and persuaded themselves that they could in fact cause us to acquiesce in whatever it is they wanted to do," he said. "The United States is not going to do that, President (George W.) Bush is not going to do that."

Rumsfeld's comments came after Bush said he would seek $87 billion for fighting terrorism and rebuilding efforts in Iraq and Afghanistan. He spoke also just three days before the second anniversary of the attacks on New York and Washington, which the United States blames on al Qaeda Islamist militants.

CHEMICAL WEAPONS

U.S. soldiers are attacked almost daily in occupied Iraq and are fighting efforts by Taliban fighters to regroup in Afghanistan. They are also hunting ousted Iraqi president Saddam Hussein and al Qaeda leader Osama bin Laden.

Democratic criticism of the Republican administration's invasion of Iraq and post-war rebuilding efforts complicated efforts to try and get the message out that progress was being made, Rumsfeld said. "It does complicate it, it makes it more difficult, but I guess that's life," he said.

Critics note the United States has so far failed to produce any evidence of the production of weapons of mass destruction though this had been cited as the main reason for the March invasion of Iraq and overthrow of Saddam.

Rumsfeld met briefly in Baghdad with former U.N. weapons inspector David Kay, who is coordinating the hunt for the banned weapons. But he said the half-hour discussion centered on what assistance the Defense Department could provide rather than a review of the information being collected.

"We did not have much of a discussion on the substance of what he is turning up," Rumsfeld said. "I did not go into the half hour meeting and say 'OK lay out what you've found'. I went in assuming he'll (Kay) tell me if he's got something that he thinks I need to know."

© 2003 Reuters Ltd