"Yesterday in the city of Mosul, the careers of two of the regime's chief henchmen came to and end," the president, speaking in the Rose Garden. "Saddam Hussein's sons were responsible for the torture, maiming and murder of countless Iraqis."
"Now more than ever all Iraqis can know that the former regime is gone and will not be coming back," he said.
Details emerged about the raid that killed the sons. It took U.S. forces several hours and three attempts to kill the sons and two other Iraqis, said Lt. Gen. Ricardo Sanchez.
While celebrating the successful raid, Sanchez stressed that "the war goes on." Indeed, two U.S. soldiers were killed in separate attacks, and Arab TV aired a new audiotape supposedly of Saddam urging Iraqi soldiers to attack Americans.
In key developments:
The president hailed progress since the end of major combat in Iraq, including the formation of local councils, Tuesday's visit to the United Nations by a new national council, the upcoming formation of both a new Iraqi army and a new constitution.
The president said the coalition that invaded Iraq "has a comprehensive strategy to move Iraq to a future that is secure and prosperous…for the good of Iraq and for the security of the United States and our friends."
"A few remaining holdouts are trying to prevent the advancement of hope and freedom," Mr. Bush said. "These killers are the enemies of Iraq's people. They operate mainly in a few areas of the country and wherever they operate they are being hunted and they will be defeated."
The deaths of Saddam's 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.
However, Abdul Bari al Atwan, editor of the Arabic newspaper Al Quds, told the CBS News Early Show, "I disagree with the opinions that this will actually make Iraq safer and put an end to the resistance. I believe it will fuel the resistance."
Tuesday's raid began when an Iraqi informer walked into a U.S. military location in Iraq Monday night and provided information that the two brothers were staying in a villa on the north side of Mosul.
But, reports CBS News Correspondent Jim Stewart, sources say U.S. intelligence had already sniffed out the same lead and the tipster only confirmed their suspicions.
After getting the tip, U.S. forces moved elements of the 101st airborne, an infantry company, Kiowa helicopters and Humvees with TOW antitank systems and .50-caliber machine guns into the area. Iraq police formed a cordon.
AH-64 Apaches and Air Force A-10s were on standby but weren't used because of fears civilians might be harmed, Sanchez said.
When U.S. troops first entered the building, they met fire as they mounted the stairs to the second floor. Three soldiers were wounded on the stairs and one outside. The troops pulled back.
U.S. forces then began to "prepare the objective prior to reentry," Sanchez said, pounding the building with rockets and .50-caliber machine gun fire.
After the second attempt to enter was repulsed, ten antitank missiles were fired into the structure, apparently killing three of the men inside. Troops entered for the third time, climbed to the second floor, took fire, and killed the remaining person.
According to Sanchez, no civilians were injured in the raid.
U.S. forces used dental records and four individuals - including No. 4 on the most wanted list, Abid Hamid Mahmoud al-Tikriti — to confirm the identities of the sons. Central Command is now working on ways to prove to Iraqis the sons are dead. Asked if that might include photographs, Sanchez said all options were open.
Hours after the raid, 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.