"We are certain that Odai and Qusai were killed today," said Lt. Gen. Ricardo Sanchez at a news conference in Baghdad. "The bodies were in such a condition where you could identify them."
Four coalition soldiers were wounded and two other Iraqis were killed in the raid, but Saddam was not among them. The house belonged to one of Saddam's cousins, a key tribal leader in the region.
The deaths of the sons could have a major impact on the Iraqi resistance, which has been mounting about a dozen attacks a day against U.S. occupation troops. The guerrillas are thought to be 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.
Odai and Qusai 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 U.S. military commander in Iraq says a walk-in tipster revealed their hideout, but top officials in Washington tell CBS News multiple intelligence sources pinpointed the brothers.
In Washington, L. Paul Bremer, Iraq's top civilian administrator, said he did not want to comment on how the deaths of Saddam's sons would affect security in Iraq.
However, Bremer said: "It certainly is good news for the Iraqi people."
"This will contribute significantly to reducing attacks on coalition soldiers," said Ahmad Chalabi, a delegate from the Coalition Provisional Authority, speaking at the United Nations.
Asked whether the killing of the sons would reduce the incessant attacks on American forces, 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," Sanchez said.
Hours after the raid in Mosul, gunfire erupted throughout Baghdad, making travel very dangerous. The shooting was believed to be celebratory as news of the killing of the sons spread through the capital.
"It's probably very appropriate that they would be celebrating about now," Sanchez said.
Fighting broke out after soldiers from the 101st Airborne Division surrounded the stone, columned villa.
When troops 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," Sanchez added.
After the firefight, about 1,000 people gathered, some expressing delight, others cursing the Americans.
The soldiers removed four bodies and did not let photographers near enough to take pictures.
Some Mosul civilians appeared to have been caught in the crossfire. It was not known how many people were injured, but several were taken to a hospital.
Officials gave conflicting reports on whether anyone was captured during the assault. The officials said they had no initial information that would suggest Saddam was present during the raid.
Experts conducted DNA tests after the bodies were flown from Mosul to another location, officials said.
Throughout the day, Defense Secretary Donald H. Rumsfeld briefed President Bush personally about the assault.
Qusai, Saddam's younger son, was his father's likely successor, U.S. intelligence officials said. He ran much of Iraq's security apparatus, controlling several militias, internal security services and the military forces of the once-vaunted Republican Guard.
He was described as quiet and level, particularly compared to Odai, Saddam's eldest son, 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 ongoing guerrilla campaign in Iraq.
Odai also controlled information and propaganda in Saddam's Iraq, 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 town 240 miles northwest of Baghdad that housed Iraqi army bases, is outside the so-called "Sunni Triangle" in central Iraq home to much of the remaining support for Saddam, a Sunni Muslim who used his Baathist Party to oppress the country's Shiite majority.
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.
In other developments: