The American military in Iraq says extensive tests confirm that Saddam Hussein's sons were killed in an attack by US forces on a villa in the northern city of Mosul.
Two hundred US troops attacked the villa in Mosul
The leader of US-led coalition ground forces in Iraq said dental records and independent positive identifications by four former regime officials showed that two bodies recovered from the villa were Qusay and Uday Hussein.
Lieutenant General Ricardo Sanchez also said that the injuries on one of the bodies matched those on Uday's X-ray records, taken after an assassination attempt crippled him.
"We have no doubt that we have the bodies of Uday and Qusay," he told reporters at a briefing in the Iraqi capital Baghdad.
In Washington, US President George W Bush said the death of the brothers was proof that "the regime is gone and it will not be coming back".
And he said the US would "keep its promise to destroy every remnant of the regime".
But hopes that news of the brothers' deaths would sap the morale of those launching attacks on US forces in Iraq received a blow early on Wednesday morning when two American soldiers were killed and eight injured in two separate incidents.
Meanwhile, Dubai-based al-Arabiya television is broadcasting what is said to be a new audiotape message from Saddam Hussein to the Iraqi people, apparently recorded three days ago.
As in previous messages, the speaker urges resistance against the occupying coalition forces in Iraq.
Saddam Hussein's sons were numbers two and three on America's 55-strong "most wanted Iraqis" list. Their father remains at large.
At the same briefing, General Sanchez also revealed that number 11 on the list - the commander of Saddam Hussein's Special Republican Guard, Barzan Abd al-Ghafur al-Tikriti - had now been picked up.
'Arrest attempts resisted'
The bodies of the former Iraqi leader's sons are said to have been flown to Baghdad's international airport from Mosul.
They died barricaded in a fortified second-floor section of a three-storey villa in northern Mosul after two attempts by coalition forces to arrest them had been resisted, according to General Sanchez.
Heavy gunfire injured four US troops and forced a withdrawal by the American forces, who were tipped off about the brothers' presence by an Iraqi informant.
Helicopter gunships, armoured vehicles and ground troops then opened fire on the building.
General Sanchez said Qusay, Uday and "another adult" - reportedly a bodyguard - were probably killed by a hand-held missile fired by ground troops.
As US troops entered the building for the final assault, General Sanchez said, they came under fire from a "remaining individual" - who was shot dead.
Reports suggest that Qusay's 14-year-old son was among the group of four people in the fortified section of the building.
The coalition is under pressure to allow television cameras to film the dead men, to dispel any doubts that may exist about their demise.
General Sanchez said this was under discussion.
In the latest deadly attacks on US forces, two military convoys - one near Mosul, the other in Ramadi, west of Baghdad - were hit by what the US military described as "improvised explosive devices".
BBC defence correspondent Jonathan Marcus says nobody should be in any doubt that attacks against US forces in Iraq will continue, and could even intensify.
But he adds that Uday and Qusay's deaths, if exploited properly, could mark a much-needed turning-point in the American occupation.
Reports of the deaths of the two men - among the most influential and most feared in the former regime - were greeted on the streets of Baghdad by people across the city firing shots into the air.
However, there is also deep scepticism about the Americans' announcement of the brothers' deaths in the city.
The news was welcomed by US President George W Bush and British Prime Minister Tony Blair, who have been under pressure over the failure of their forces to find weapons of mass destruction in Iraq following the war that toppled Saddam Hussein.
Correspondents say the Iraqi who tipped off the US military stands to gain at least part of two bounties - each worth $15m - which Washington placed on the heads of Uday and Qusay.
There are reports that the Americans received the information that led to the brothers from the villa's owner - said to be a cousin of Saddam Hussein and local tribal leader.
A senior US officer said the informant was in "protective
custody" in Iraq. When asked why, Colonel Joe Anderson of the 101st Airborne Division said: "People know who owns the house, so that's a factor."
Qusay, 36, had become Saddam Hussein's heir apparent and controlled key areas of the country's security apparatus.
Uday, 39, controlled much of the media and was centrally involved in the illegal international trade which helped keep the regime in power.
He had a reputation for brutality rivalled only by that of his father's.