The statement from the commander, Lt. Gen. Ricardo S. Sanchez of the Army, came on a day in which 20 American soldiers were wounded and one was killed in five separate attacks.

One American soldier was killed and 10 were wounded in two attacks in central Iraq on Thursday night, the American military said today.

The American soldier who was killed was shot by a sniper in Baghdad, while the 19 American soldiers were wounded in a mortar attack near the town of Balad, north of the capital, a military spokesman said.

With the violence seemingly escalating daily, the offer of a bounty for Mr. Hussein seemed to reflect the renewed urgency allied officials and military commanders attach to finding the deposed leader and his two sons, whose specter they believe is fueling the growing resistance to the American occupation.

"Until we know for sure, their names will continue to cast a shadow of fear over this country," L. Paul Bremer III, the American civilian administrator of Iraq, said on Thursday in his weekly address to the Iraqi people.

In Washington on Thursday, a group of senators just back from a three-day visit to Iraq were even more emphatic about the need to capture or kill Mr. Hussein.

"There's a pervasive climate of fear that is impeding the recovery, particularly in central and southern Iraq," said Senator Susan Collins, a Maine Republican. "There is a fear that he will return, that he will come back. And that fear prevents us from making progress as rapidly as we otherwise would, and that fear emboldens those who would attack our troops."

The $25 million reward for Mr. Hussein is the same amount offered for Osama bin Laden, the leader of Al Qaeda. Mr. Bremer said up to $15 million apiece would be offered for similar information on Mr. Hussein's sons, Uday and Qusay.

Mr. Bremer said in an interview on Sunday that the "general assessment" of people he talked to was that Mr. Hussein was still in Iraq. 

While Mr. Bremer maintained that the threats and violence against American soldiers and civilians, as well as the Iraqis working with them, would not deter reconstruction, General Sanchez made clear at a news conference Thursday that rebuilding the country and fighting the enemy would have to take place side by side. 

While saying the daily attacks on American forces did not appear to be centrally coordinated, the general acknowledged that there had been an "increase in sophistication of the explosive devices." He said 25 soldiers had been killed in action and 177 wounded since May 1, when Mr. Bush declared the official cessation of major hostilities. 

The multiple attacks came a day after Mr. Bush seemingly invited confrontation with militant Iraqis, saying, "Bring 'em on." The American-led alliance, he said, has adequate force to deal with the security situation. 

Thursday's attacks seemed to defy that assertion. They also suggested that sapping the resistance might not be as simple as capturing or killing Mr. Hussein. The attacks occurred in diverse locations: a Sunni area west of Baghdad that staunchly supported the former government, a Shiite neighborhood in Baghdad that did not and the center of the city. 

In the Baghdad neighborhood of Kadhimiya on Thursday, a gunman opened fire on a group of soldiers from the First Armored Division on foot patrol at 2:30 a.m., wounding one of them. The soldiers returned fire, killing the gunman and wounding a 6-year-old boy with him, according to an American military spokesman.

In the city of Ramadi, about 65 miles west of Baghdad, six soldiers were wounded when their two-vehicle convoy drove over an improvised explosive device at 6:30 a.m. Thursday.

Ramadi has become a center of resistance to the American-led occupation. It is about 30 miles west of Falluja, where an explosion at a Sunni mosque killed at least six people on Monday night. An allied investigation blamed a bombmaking class being held in a building adjacent to the mosque, but many residents accused the Americans of firing a missile into the mosque and promised revenge against American troops.

In Baghdad, just before 10 a.m. on Thursday, a man on foot fired a rocket-propelled grenade at a three-vehicle military convoy moving down Haifa Street, a busy thoroughfare. One Humvee was struck, wounding three soldiers, witnesses and a military spokesman said. 

Witnesses also said that in response, soldiers in one of the other vehicles opened fire indiscriminately, seriously wounding, and possibly killing, at least one Iraqi driver nearby. Blood pooled next to the driver's blue car soon after the attack.

The attack suggested that the urban warfare that had so concerned military planners before the fall of the Hussein government was materializing in unexpected forms. The attack against the convoy on Haifa Street was at least the second rocket-propelled grenade assault in Baghdad during daylight hours this week.

In both cases, the attackers escaped. Whether out of fear or sympathy for their cause, bystanders and witnesses have done nothing to help allied forces apprehend attackers. 

Soldiers who arrived at the scene of the Haifa Street attack in Baghdad this morning crouched by their vehicles or pointed their weapons at the high-rise apartment buildings lining that section of the street. In the distance, an AK-47 rifle sounded. 

A crowd of people gathered around the destroyed Humvee and looted it, taking whatever they could remove. Children and adults climbed on top, stomping on it and chanting, "God bless Muhammad!" Then someone set the vehicle on fire, and the crowd backed away, watching it slowly burn. Children hurled stones at the blazing vehicle.

More American reinforcements arrived to clear the crowd and guard the vehicle. An armored vehicle drove through and paused, training its gun first on the crowd and then on the apartments above. Helicopters circled low overhead. 

Some bystanders expressed support for the attack. "All men should fight," Nidhal Latif Tawfiq said. "If I wasn't a woman, I would go to that car," she said of the Humvee surrounded by looters. "I have no job." 

The crowd's ire seemed to be fueled as much by a lack of jobs and electric power in Baghdad — most parts of the city still have no more than 8 to 10 hours of electricity a day — as by anti-American sentiment. 

"It's not because of Saddam that people are doing these things," one man said. "It is because there's no government, there's no electricity and just false promises." 

A 12-year-old boy, Ghanim Hamid, carrying part of a military food ration taken from the Humvee, asked if it was true that the Americans were withholding water and power from the Iraqis because Iraqis were shooting at the troops. 

"Get out from our country," someone had scrawled on a wall nearby. It was written in English, so for the soldiers passing by there would be no mistaking its meaning.