But a U.S. source close to the search said that could well mean the missing soldiers are still somewhere inside the search zone, reports CBS News correspondent Mark Strassmann, and their captors feel the pressure.
The U.S. military also said for the first time it believes the three missing soldiers were abducted by al Qaeda-linked militants after an attack that included three roadside bombs.
"What you are doing in searching for your soldiers will lead to nothing but exhaustion and headaches. Your soldiers are in our hands. If you want their safety, do not look for them," the Islamic State of Iraq said on a militant Web site.
The insurgents suggested they attacked the U.S. convoy as revenge for the rape and murder of a local teenager last year.
"You should remember what you have done to our sister Abeer in the same area," the statement said, referring to five American soldiers who were charged in the rape and killing of 14-year-old Abeer Qassim al-Janabi and the killings of her parents and her younger sister last year.
Three soldiers have pleaded guilty in the case — one of the most shocking atrocities committed by U.S. troops in the Iraq war.
Three U.S. soldiers have been missing since Saturday, since a deadly attack on their convoy in Mahmoudiya, about 20 miles south of Baghdad. The attack also killed four U.S. soldiers and an Iraqi soldier, according to the military, which had described the Iraqi as an interpreter.
Military sources tell CBS News that all the soldiers were from thee 2nd Brigade, 10th Mountain Division, based at Fort Drum, New York. All of the families have been notified of the deaths, and the unknown status of the missing troops.
On Sunday, the Islamic State of Iraq claimed that it had captured U.S soldiers in the deadly attack in the Sunni area, which is known as the "triangle of death" and is an al Qaeda stronghold.
If the claim proves true, it would mark one of the most brazen attacks by the Islamic State of Iraq, a coalition of eight insurgent groups, including al Qaeda in Iraq.
In Other Developments:
About 4,000 U.S. troops backed by aircraft, intelligence units and Iraqi forces have been scouring the farming area around Mahmoudiya and the nearby town of Youssifiyah for three days, as the military promised to make every effort available to find the missing soldiers.
On Monday, U.S. military spokesman Maj. Gen. William B. Caldwell, IV said: "At this time, we believe they (the three soldiers) were abducted by terrorists belonging to al Qaida or an affiliated group, and this assessment is based on highly credible intelligence information."
Lt. Col. Christopher Garver, another U.S. military spokesman in Baghdad, pointed out earlier Monday that the terror network also had claimed responsibility for killing two U.S. soldiers whose mutilated bodies were found in the same area last year.
Late last month, the group named a 10-member "Cabinet" complete with a "war minister," an apparent attempt to present the Sunni coalition as an alternative to the U.S.-backed Shiite-led administration of Prime Minister Nouri al-Maliki.
The family of Army Sgt. 1st Class James David Connell Jr., 40, of Lake City, Tenn., said he was among one of the four soldiers killed in the attack near Mahmoudiya.
Four U.S. troops were killed in three separate attacks in Baghdad and south of the capital on Monday, while a fifth soldier died of non-combat related causes, the military said. The deaths raised to at least 3,398 the members of the U.S. military who have died since the beginning of the Iraq war in March 2003, according to an Associated Press count.
A roadside bomb near the southern city of Basra also killed one Danish soldier and wounded five, according to Maj. Kim Gruenberger of the Danish Army Operational Command. An Iraqi translator also was wounded.
Seven Danish soldiers have been killed in Iraq since the war began. In February, the Danish government said it would withdraw its 460-member contingent from Basra by August and replace it with a smaller helicopter unit.
In Mahmoudiyah, residents complained on Monday that coalition forces had searched through their homes, and AP Television News footage showed on one apartment that appeared to have been ransacked in the search.
One man said three residents in the area, including two guards at a local mosque, had been detained by coalition forces, but that could not be immediately confirmed.
U.S. and Iraqi forces also exchanged fire with gunmen near the town of Youssifiyah during the house-to-house search operation for the missing American soldiers, killing two suspected insurgents and injuring four others, a top Iraqi army officer in the area said.
He said the fighting began at about 3:30 a.m. and lasted for about 30 minutes. The officer, who spoke on condition of anonymity due to security concerns, said the coalition's search operation in the region has detained more than 100 suspects. The U.S. military did not immediately comment on the report.
Deadly violence also struck other areas of Iraq on Monday.
The worst attack occurred in the Diyala capital of Baqouba, 35 miles northeast of Baghdad, when gunmen in two cars opened fire on a police checkpoint, killing three policemen and two civilians, police said. Two policemen and four civilians were wounded in the 9:30 a.m. attack, which ended when the assailants fled the scene, police said.
On Sunday, five civilians were killed execution style on the streets of Baquoba by gunmen who appeared to be accusing them of collaborating with the U.S.-led coalition.
The U.S. military has noted an uptick in violence in the volatile region and sent 3,000 additional forces to try to tame the violence.