WASHINGTON - Top U.S. officials oppose sending more troops to Iraq, citing better intelligence and increased cooperation with Iraqis as keys to countering the rising number of terrorist attacks that have hampered rebuilding efforts.

L. Paul Bremer, the U.S. civilian chief in Iraq, and Gen. Richard Myers, chairman of the Joint Chiefs of Staff, also welcomed more assistance from other countries to help stabilize the situation. But they stopped short Sunday of relenting to foreign critics calling for some military control to be ceded to the United Nations.

Bremer told "Fox News Sunday" it was "hard for me to see how the U.N. itself can play a further military role because the U.N., in my experience, normally insists on commanding its own troops."

At least some U.N. control is a condition that France, India and other nations have insisted on before sending troops. Bremer said all military forces should remain under command of the U.S.-led coalition, although "the U.N. clearly has a vital role to play in the reconstruction of Iraq."

Questions about U.S. troop strength in Iraq have heightened since the truck bombing of U.N. headquarters in Baghdad last week that killed the United Nations' top envoy and at least 23 others.

About 150,000 American troops are in Iraq, along with 20,000 soldiers from Britain and other coalition countries. Roughly 50,000 Iraqis are working with the United States on security matters.

There were fresh signs of unrest Sunday, after a bomb exploded outside the house of one of Iraq's more important Shiite clerics, killing three guards and injuring 10 others.

Also Sunday, the International Committee of the Red Cross said it was scaling back its work force in Baghdad after receiving warnings that the organization might be a terror target.

Myers said on CBS' "Face the Nation" that Gen. John Abizaid, the U.S. military commander in Iraq, hasn't asked for more troops, but the Pentagon would consider any such request.

Bremer, interviewed on ABC's "This Week," also cited the need to reconfigure U.S. forces to make them more mobile as another way to stem the violence.

American officials believe militants from Saudi Arabia, Syria and Iran are infiltrating Iraq to attack Western interests. Last week, President Bush said more foreign "al-Qaida-type fighters" have moved in.

Myers told NBC's "Meet the Press" that the United States has not created a haven for terrorists, though he maintained that Iraq was a big part of the broader war on terrorism.

"And what the terrorists want to do is they want to have their way," the general said. "And that's just not going to be. It's more a question of wills right now."

Concerns over how big a role other countries should play in policing Iraq have also risen because of increased criticism about overall U.S. military strength. Besides Iraq, the United States has long-term commitments in - among other places - South Korea, Kosovo and Afghanistan, and recently deployed a small peacekeeping force to Liberia.

Defense Secretary Donald H. Rumsfeld, in an interview with Time magazine, said, "The analysis thus far says that we have sufficient forces to do the assigned missions," although the Pentagon is working on proposals to make the military more efficient.

Sen. Joseph Biden, D-Del., cited some outside estimates that an additional 40,000 to 60,000 soldiers would be needed in Iraq.

"In order to get those, we need a U.N. resolution authorizing them. We don't have to have these folks under blue helmets (U.N. command). They can be under U.S. command," said Biden, senior Democrat on the Senate Foreign Relations Committee.

People with specialized skills, such as linguists or workers who could help rebuild oil refineries and other infrastructure, are especially needed, said Sen. John McCain, R-Ariz., a member of the Senate Armed Services Committee.

Despite the continuing violence, Bremer insisted that the effort to defeat terrorists and rebuild Iraq would not be deterred.

"We can't duck this fight," he said. "It's a fight, as we saw on Tuesday (with the U.N. bombing), against the international community and against the world