An audiotape purportedly from ousted Iraqi leader Saddam Hussein said his sons Uday and Qusay died as martyrs for Iraq.
The US insists it is closing in on Saddam Hussein
CIA analysts said the tape, which was broadcast by al-Arabiya satellite television a week after the deaths, was highly likely to be authentic.
"Brothers and sons, I mourn to you, and I convey to you the glad tidings... that the souls of another group of martyrs have ascended to their creator," the taped speaker says in Arabic.
"Beloved Iraqis, your brothers Uday and Qusay, and Mustafa, the son of Qusay, took a stand of faith, which pleases God."
The speaker praises a "valiant battle with the enemy that lasted six hours", and - in common with earlier tapes attributed to Saddam Hussein - urges resistance to US-led occupation forces in Iraq.
He adds that even if he had 100 children other than Uday and Qusay, he would offer them in the same way.
It is the fifth recording attributed to Saddam Hussein since the Iraqi capital Baghdad fell to US-led troops on 9 April.
If authentic, his words could end lingering doubts among some Iraqis about whether the men killed by US troops in the northern city of Mosul and whose bodies were shown on television were indeed Uday and Qusay Hussein.
A CIA official said that analysts concluded there is a "high likelihood" that the voice on the tape was that of Saddam Hussein.
It follows a tape aired by al-Arabiya television last week claiming to be from Saddam Hussein, which US officials said was also likely to be genuine.
The BBC's Heba Saleh says the former Iraqi leader may be hoping his broadcasts will strengthen the resolve of loyalists to his Baath party, believed by the US to be behind a spate of attacks on American soldiers.
But she adds that the messages are unlikely to have an impact outside Iraq - although most Arabs are delighted with what they consider to be the Iraqi resistance, they do not believe people are fighting for the ousted dictator.
Washington says the net is closing in on the former president following the deaths of his feared sons.
In a dawn raid on Tuesday, US forces rounded up a number of people in the deposed leader's hometown of Tikrit, including a man they said was a bodyguard and long-time associate of the ousted leader, Adnan Abdullah Abid al-Musslit.
US Deputy Secretary of State Richard Armitage said on Monday that troops carrying out such raids in Iraq "were just hours behind Saddam Hussein".
Mr Armitage told CNN that although the US was keen to capture the ousted leader alive, if such an action posed a risk to US troops they would kill him without hesitation.
On Tuesday, rumours that Saddam Hussein had been captured sparked a surge in US stocks.
The Pentagon has said it has no information to confirm them.
Uday and Qusay were killed when US forces raided a house in Mosul on 22 July.
The US took the unprecedented step of showing their pictures and allowed the media to film their bodies, in an effort to quash Iraqi doubts about their identity.
The release of the photos and footage caused much debate in Washington and on Arabic television.
The US does not normally publish pictures of dead combatants and raised strong objections when dead US troops were shown on the Arabic al-Jazeera TV channel during the war.
But US Defence Secretary Donald Rumsfeld said publication of pictures would save American and coalition lives and prove that Iraq's former rulers would never return.