A front group for Al Qaeda warned America yesterday to halt its expanding search for three missing American soldiers “if you want their safety.” The Pentagon acknowledged for the first time that it believes the servicemen are in terrorist hands.

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 Qaeda, 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 yesterday, chief U.S. military spokesman Major General William Caldwell said the U.S. 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 Qaeda 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 America soldiers in Iraq since March 23, 2003, when Private Jessica Lynch and six others were captured in an ambush near Nasiriyah in which 11 Americans were killed.

Al Qaeda 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.