U.S. Maj. Gen. William Caldwell said four raids had been carried out since Friday's attack and that ground forces, helicopters and airplanes were taking part in the search.
He said a dive team also was going to search for the men, whose checkpoint was located by a Euphrates River canal near Youssifiyah, 12 miles south of Baghdad.
The New York Times reported that Iraqi residents in the area said they saw two soldiers taken prisoner by a group of masked guerrillas. It said the two surviving soldiers were led to two cars and driven away.
Fellow soldiers at a nearby checkpoint heard small-arms fire and explosions, and a quick-reaction force reached the scene in 15 minutes, the military said. The force found one soldier dead but no sign of the two others.
"We are currently using every means at our disposal on the ground, in the air and in the water to find them," said Caldwell, the spokesman for U.S. forces in Baghdad.
The area is known as the Triangle of Death because of the frequent ambushes and attacks against U.S. soldiers and Iraqi troops.
The spokesman noted the military was still searching for Sgt. Keith Matthew Maupin, who went missing on April 9, 2004.
"We continue to search using every means available and will not stop looking until we find the missing soldiers," he said.
Maupin was captured when insurgents ambushed his fuel convoy with the 724th Transportation Co. west of Baghdad. A week later, Arab television network Al-Jazeera aired a videotape showing Maupin sitting on the floor surrounded by five masked men holding automatic rifles.
That June, Al-Jazeera aired another tape purporting to show a U.S. soldier being shot. But the dark, grainy tape showed only the back of the victim's head and did not show the actual shooting. The Army ruled it was inconclusive whether the soldier was Maupin.
A 20-year-old private first class at the time of his capture, Maupin has been promoted twice since then.