US Central Command has reported that assailants armed with rocket-propelled grenades had killed an American soldier and critically wounded another in the Iraqi capital.
The attack, aimed at soldiers collecting arms at a checkpoint, took the number of US personnel killed since April 9, when Baghdad fell to the Americans, to at least 40.
"Do I think that's going to disappear in the next month or two or three? No. Will it disappear when some two or three divisions of coalition forces arrive in the country? No," Donald Rumsfeld told a news conference in Lisbon.
"It will take time to root out the remnants of the Saddam Hussein regime and we intend to do it."
The US military said today that US troops had staged raids Monday to crack down on guerrilla fighters north of Baghdad, detaining 384 people and suffering four wounded.
With Iraq's political future still in question, a scion of Arabia's Hashemite dynasty, Sharif Ali bin Hussein, returned to Iraq Tuesday, 45 years after a revolution toppled the British-backed monarchy and killed his cousin, King Faisal II.
A multinational force that will seek to keep the peace in the devastated country is beginning to take shape. An advance unit of 35 Italian troops flew into the southern city of Basra Tuesday.
A Qatari plane with relief supplies also arrived there on what was billed as the first commercial flight to postwar Iraq.
The United States has said its failure to find Saddam may be emboldening the fallen leader's Baath party supporters to attack US forces in Iraq. The former Iraqi president has not been seen since the fall of Baghdad.
"It might give heart to the Baathists who may want to hope that they can take back that country, which they are not going to succeed in doing," Rumsfeld said late on Monday.
"We'll just keep looking for him. We'll find him," he told reporters on the flight to Portugal at the start of a four-day European tour.
Rumsfeld said Saddam sympathisers in the north of the country were behind the string of attacks on U.S. forces. "There is no one who thinks that it's a well-organised nationally directed campaign," he said.
At yesterday's news conference, Rumsfeld said Iraqis were being recruited in large numbers to help foil the attackers.
"We are bringing on board continuously hundreds and most recently thousands of Iraqis who are participating in joint patrols," he said.
"So the idea that there won't be any help until coalition countries arrive in the fall is exactly false, because the security situation in the country is improving as we proceed."
The Italian unit that arrived in Basra is the advance guard of a 1,700-strong Italian peacekeeping contingent due by the end of June. It will come under British control.
A British military spokesman said an advance party of Dutch troops was due in Basra Thursday. The Netherlands is to send 1,100 marines to the British-controlled zone in southern Iraq.
More than 10 countries have also pledged troops for a 7,500-strong Polish-led force to be deployed in south-central Iraq. There are currently 146,000 U.S. troops and about 14,000 international troops in Iraq, according to Rumsfeld.