The names of the soldiers, who are from the 2nd Brigade Combat Team of the Army's 82nd Airborne Division, are being withheld until their relatives have been notified.
The attack in Baghdad - the 11th death of a U.S. soldier in just 15 days - is the latest in a series of attacks on U.S. troops assigned to keep the peace in Iraq, especially in the city of Fallujah, where there have been ambush attacks on an almost daily basis.
The pattern of the attacks and the consistent use of rocket-propelled grenades has raised suspicions that the ambush hits are being coordinated and carried out by remaining resistance groups still loyal to Saddam Hussein, or at least his legacy.
The attacks prompted an Iraqi exile to insist, during a recent speech in New York, that the felled dictator is not only still alive in Iraq, and is offering bounties for killing Americans. The Pentagon did not support the claim, saying there was still no evidence to confirm whether Saddam is dead or alive.
But as CBS News Correspondent Mark Phillips reports, for the soldier whose life is on the line — it hardly matters whether the Iraqi shooting at him is getting orders from a centralized resistance command structure or whether he's acting on his own.
Although there is growing evidence that the attacks are being organized on at least a regional level by remnants of Saddam Hussein's regime.
The attacks are becoming more frequent, and claiming more American lives. According to Central Command, another U.S. soldier was killed Tuesday when attackers fired rocket-propelled grenades at American troops at a collection point for illegal weapons in southern Baghdad.
Colonel David Perkins, who has been functioning as the effective mayor, police chief and chief enforcer of Fallujah, said, "If you have an American flag on your shoulder, you're a target."
It is Perkins' men who have been sent into Fallujah to try to pacify it. The official line on the attacks is that they are isolated incidents committed by Saddam loyalists.
"I believe these are localized, decentralized attacks," said Lt. Gen. David McKiernan, a U.S. commander in Iraq.
But the experience in the field seems to be different. In Fallujah, the grip of Saddam's now outlawed Ba'athist Party is still felt.
"The Ba'athist party had very long tentacles and it was throughout the country, so while they may not be coordinating directly throughout the country, they are at least coordinating regionally," said Perkins.
Whether these attacks are part of a coordinated national effort or merely isolated incidents is almost irrelevant — the effect is the same. They're happening all across the country.
In fact, the more disjointed they are the more difficult it will become to cut off the head of the beast and snuff them out. Especially as the fate of Saddam Hussein himself is still unknown.
Saddam's last public appearance — or a Saddam double — in the final days of the war is still taken by loyalists as proof he survived the conflict. And only finding him, or proving he's dead may take the backbone of those still fighting his war.