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Saddam Hussein's sons Odai (search) and Qusai (search) were killed Tuesday when U.S. soldiers stormed a house in the northern Iraqi city of Mosul, U.S. military officials said Tuesday.

The six-hour raid was the most successful American operation since the war and comes as a much-needed tonic for U.S. troops, who recently have suffered a dozen attacks a day by Saddam loyalists and other anti-American groups.

Though many thought the demise of Saddam's sons would put an end to many of the attacks on coalition troops, two U.S. soldiers were killed and eight wounded in separate ambushes Wednesday -- including one on the outskirts of Mosul where the sons were slain the day before.

News of the sons' deaths touched off celebratory gunfire in Baghdad and at least one southern city. But L. Paul Bremer (search ), Iraq's top civilian administrator, cautioned "there will be some people who will be pretty unhappy that we killed these two guys."

"If one of my sons was dead, I'd want somebody to pay for it," Sgt. Colin Frederick, a 23-year-old armored scout from Fort Carson, Colo., said while patrolling the dangerous "Sunni Triangle," a bastion of Saddam loyalists stretching north and west from Baghdad. Most attacks on U.S. forces since the end of the war have been launched in the region.

The bodies of Odai and Qusai -- long feared by most Iraqis for their roles in the military and intelligence arms of Saddam's brutal dictatorship -- were taken to Baghdad International Airport (search) Wednesday to be flown out of the country, American officials said. They would not say why the bodies were being taken out of Iraq or to where.

In the midst of the confusion, a U.S. soldier mistakenly shot a man and a girl who was about six. U.S. soldiers came upon the man as he was shooting his gun and returned fire, thinking they were under attack.

Bremer confirmed to Fox News that the Iraqi who provided the information that led to the raid will get the full reward of $30 million -- $15 million for each son. "I'm looking forward to giving that guy a check for 30 million dollars," he said.

Four coalition soldiers were wounded and two other Iraqis were killed in the raid, but Saddam was not among them. The house belonged to Nawaf al-Zaydan Muhhamad, a Saddam cousin and tribal leader in the region.

• Map: Postwar Iraq

"We are certain that Odai and Qusai were killed today," Lt. Gen. Ricardo Sanchez (search ) told reporters in Baghdad. "The bodies were in such a condition where you could identify them."

The identifying marks included Odai's scars from a 1996 assassination attempt, a senior defense official said, speaking on condition of anonymity.

Fox News has learned that Abid Hamid Mahmud Al-Tikriti (search ), Saddam's top aide who surrendered June 17 and was the ace of diamonds in the U.S. military's deck of cards representing Iraq's most wanted former leaders, provided some of the information leading U.S. officials to confirm that two of the bodies were Odai and Qusai.

The soldiers removed four bodies and did not let photographers take pictures. The other two bodies were tentatively identified as that of a bodyguard and a teenager, U.S. officials said. The teen may have been a son of Qusai and grandson of Saddam, U.S. officials said.

The daily attacks on U.S. occupation troops are thought to be the work of former military officers and Baath Party leaders loyal to Saddam and his family -- especially the sons, who played primary roles in the military and feared security services.

"Outstanding," said 1st Lt. Greg Wilson, 33, with the Florida Army National Guard in Baghdad. He clapped his hands and said: "One step closer to getting home."

Both Odai, 39, and Qusai, 37, ranked second only to their father in the deposed regime. They were Nos. 2 and 3 on the U.S. list of 55 top former Iraqi officials wanted by Washington. The United States had offered a $25 million reward for information leading to Saddam's capture and $15 million each for his sons.

The White House applauded the action.

"Over the period of many years, these two individuals were responsible for countless atrocities committed against the Iraqi people and they can no longer cast a shadow of hate on Iraq," it said in a statement.

Secretary of State Colin Powell said, "The Iraqi people are safer today. We will pursue the other members of his murderous regime wherever they might be hiding."

British Prime Minister Tony Blair hailed the deaths as "a great day for the new Iraq." Speaking during a trip to Hong Kong, Blair said the two helped lead a regime "responsible for the torture and killing of thousands and thousands of innocent Iraqis."

Sanchez said he thought the security situation now would improve.

"I believe very firmly this will have an effect. This will prove to the Iraqi people that these two members of the Iraqi regime will never come to power again," the general said.

Ahmad Chalabi, a delegate from Iraq's new Governing Council, agreed. "This will contribute significantly to reducing attacks on coalition soldiers," he said, speaking at the United Nations.

After the firefight in Mosul, about 1,000 people gathered outside the smoldering villa, some expressing delight, others cursing the Americans.

"How can they do this?" shouted a man in the crowd, apparently more concerned with the property damage than the death of two of the cruelest men in Saddam's regime. "What are the Americans doing destroying a house like this?"

Hours later, gunfire erupted throughout Baghdad. The shooting was believed to be celebratory as news spread of the sons' deaths.

But a unit of the Florida Army National Guard, believing that it was coming under fire from 30 yards away, shot a man twice in the chest and a girl who looked to be between 6 and 8 once in the head. As the unit retreated under orders, a medic treated the girl, who was taken to a hospital in a passing car.

People in the predominantly Shiite Muslim city of Diwaniyah in the south also opened fire in celebration, shooting thousands of rounds into the air.

A bullet hit a U.S. Marine guarding a base in the city, a military official said. The official said the Marine was hit in the back and underwent surgery.

Iraqi Shiites, who are the majority in the country, were oppressed by Saddam during his 23-year rule.

The gunfight in Mosul broke out after soldiers from the 101st Airborne Division surrounded the stone, columned villa.

When soldiers approached the building, gunmen inside opened fire with small arms. The "suspects barricaded themselves in the house" and "resisted fiercely," Sanchez said. "They died in a fierce gunbattle," he added.

Soldiers from the 101st Airborne Division were working on a tip from an Iraqi informant Monday night that the sons were in the house, he said.

Asked if the United States would pay the $15 million rewards, Sanchez said: "I would expect that it probably will happen."

According to witnesses, a small force of American soldiers went to the house about 9 a.m. and asked permission to search it. The occupants refused, and the patrol withdrew until about 10 a.m., when 100 more soldiers arrived in 25 vehicles.

The Americans opened fire and took fierce return fire from inside the home, the witnesses said.

The defense official said that when U.S. troops entered the home's ground floor, they almost immediately came under fire from four people holed up in the second floor.

The home's second floor had been hardened against attack with bulletproof glass, the official said.

The U.S. soldiers then called in an Apache attack helicopter, which fired several missiles into the building, the official said.

The building, in the al-Falah neighborhood, was left charred and smoldering, its high facade riddled with gaping holes from bullets and heavy weaponry.

The interior of the house was destroyed and two adjacent homes were badly damaged.

Some Mosul civilians appeared to have been caught in the crossfire. It was not known how many were injured, but several were taken to a hospital.

Once the fighting died down, Iraqi police came to help the Americans search the building.

Experts conducted DNA tests on the bodies, which were flown from Mosul to Bayji, a northern town 25 miles north of Tikrit, officials said. But Sanchez would not answer whether the tests were positive, saying "we've used multiple, multiple sources to identify the individuals."

Qusai was probably intended as Saddam's successor, according to U.S. intelligence officials. He ran much of Iraq's security apparatus, controlling several militias, internal security services and military forces of the once-vaunted Republican Guard.

He was described as quiet and levelheaded, particularly compared to Odai, his elder brother, who had a reputation for brutality and flamboyance. Odai controlled Saddam's Fedayeen, the paramilitary force that fought U.S. troops during the war; many of its survivors are thought to be part of the guerrilla campaign in Iraq.

Odai also controlled information and propaganda, and was chairman of the country's Olympic committee.

Saddam has a third, younger son, according to some reports, and three daughters. All kept a low profile in his regime.

Mosul, a city 240 miles northwest of Baghdad that housed Iraqi army bases, is outside the so-called "Sunni Triangle" in central Iraq. It is home to much of the remaining support for Saddam, a Sunni Muslim who oppressed the Shiites.

The triangle is also a center of anti-American resistance: In the latest attack, Tuesday, a U.S. soldier was killed and another wounded in an ambush along a dangerous road north of Baghdad. His death brought to 153 the number of U.S. troops killed in action since the March 20 start of war, six more than during the 1991 Gulf War.

Ret. U.S. Army Maj. Gen. Paul Valleley, a Fox News military analyst, said he hoped Tuesday's events might lead to the ultimate capture of Saddam himself.

"One event can lead to the other," Valleley said. "So hopefully, this will lead to determining in some way where Saddam may be."

Fox News' Jim Angle, Bret Baier, Wendell Goler, Greg Palkot and The Associated Press contributed to this report.