The statements came as thousands of U.S. and Iraqi troops swept through farmhouses, fields and palm groves south of Baghdad in hopes of finding the soldiers - last seen before a pre-dawn attack Saturday in an area considered a stronghold of Sunni extremists. Four Americans and one Iraqi soldier were killed in the ambush.
For a third day, jets, helicopters and unmanned surveillance aircraft crisscrossed the skies over the sparsely populated farm area near Mahmoudiya, 20 miles south of Baghdad. U.S. and Iraqi troops - backed by dog teams - searched vehicles and pedestrians. Other teams peered into crawl spaces and probed for possible secret chambers in homes.
Residents complained of random detentions and homes being ransacked as the hunt drew in more troops and brought taunting messages from the presumed captors.
In a Web posting, the Islamic State of Iraq, an insurgent alliance that includes al-Qaida, demanded that the Americans stop the search because it will "lead to nothing but exhaustion."
"Your soldiers are in our hands. If you want their safety, do not search for them," the statement said.
It also suggested that the weekend ambush was in revenge for the rape-murder of 14-year-old Abeer Qassim al-Janabi by American soldiers in the area last year. Five soldiers have been charged in the case, and three have pleaded guilty.
"You should remember what you have done to our sister Abeer in the same very area," the statement said. "In the war against you, sometimes we win, sometimes we lose."
The message went on mock the "invincible" image of the U.S. soldier.
In a statement Monday, chief U.S. military spokesman Maj. Gen. William Caldwell said the United States was using "every asset and resource available" to find the missing soldiers.
"At this time, we believe they were abducted by terrorists belonging to al-Qaida or an affiliated group, and this assessment is based on highly credible intelligence information," he said.
If all three soldiers were taken alive, it would be the biggest single abduction of U.S. soldiers in Iraq since March 23, 2003, when Pvt. Jessica Lynch and six others were captured in an ambush near Nasiriyah in which 11 Americans were killed.
At Fort Riley, Kan., the former U.S. military commander in Iraq said soldiers could face higher chances of ambush and capture under a new strategy to shift troops into smaller outposts - part of plans to seek more outreach with Iraqi civilians and possible tips on militant activities.
"But the strategy has exposed them to greater risk of attack," said Gen. George Casey after meeting with Fort Riley and 1st Infantry Division commanders.
The redeployment of troops into the smaller bases has been strongly supported by Casey's successor, Gen. David Petraeus.
Al-Qaida has been active for years in the string of towns and villages south of the capital - a region known as the "triangle of death" after frequent attacks on U.S. and Iraqi forces as well as Shiite civilians traveling to shrine cities in the south.
Last June, al-Qaida claimed responsibility for the deaths of two U.S. soldiers whose mutilated bodies were found in the same area where the ambush occurred. Later, al-Qaida statements also linked those killings to the rape-murder of the 14-year-old girl.
Elsewhere, five other U.S. troops were killed in separate attacks Monday in Baghdad and surrounding areas south of the capital. A sixth soldier died Monday of non-combat related causes, the U.S. military said.
In another Web statement, a rival coalition of Sunni insurgent groups - the Jihad and Reform Front - accused al-Qaida of killing 12 of its senior members in Baghdad's Dora neighborhood about 15 miles north of the search area. The coalition claimed to represent the Islamic Army of Iraq, the 1920 Revolution Brigade and the Mujahedeen Army and apparently signaled new rifts within insurgent ranks in Iraq. During the search Monday, U.S. and Iraqi forces exchanged fire with gunmen near the town of Youssifiyah, killing two and injuring four, an Iraqi army officer said. The officer, who spoke on condition of anonymity because he was not supposed to release information, said about 100 suspects had been detained. The U.S. military would not comment. In a statement Monday, the U.S. command said the attack on Saturday occurred at 4:44 a.m., but a rescue force took an hour to reach the site because the area was rigged with bombs. The military said the quick reaction force found three roadside bombs hidden near the site and feared insurgents were preparing an ambush. "You can't just rush into an area ... or your first responders could become casualties as well," said spokesman Lt. Col. Christopher Garver. "You don't know if somebody is waiting there with a rocket-propelled grenade and if they shoot a helicopter down then it becomes a much bigger problem." Garver said about 4,000 U.S. troops were participating in the search operation. One of the four dead Americans was identified Monday by his family. He was Army Sgt. 1st Class James David Connell Jr., 40, of Lake City, Tenn. The area around Mahmoudiya has been especially volatile because Saddam Hussein recruited members of Sunni tribes there into his elite Republican Guard and intelligence services. Many of them were believed to have joined the insurgency after Saddam's regime collapsed in the 2003 U.S.-led invasion. U.S. officers also say extremists have fled Baghdad for surrounding areas to escape the three-month Baghdad security crackdown. Elsewhere, five other U.S. troops were killed in separate attacks Monday in Baghdad and surrounding areas south of the capital. A sixth soldier died Monday of non-combat related causes, the U.S. military said. That raised number of American service members to have died this month to 47. In southern Iraq, a roadside bomb in Basra killed one Danish soldier and wounded five other Danes and their Iraqi translator, the Danish military said. 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 other violence, at least 52 Iraqis were killed or found dead after a series of bombings, shootings and mortar attacks, all but 11 in Baghdad. AP-CS-05-14-07 1849EDT