Gen. John Abizaid, chief of the U.S. Central Command, delivered the warning Saturday to tribal sheiks and mayors in the "Sunni Triangle" city of Ramadi west of Baghdad, according to Fallujah Mayor Taha Bedawi.
"We have the capabilities and equipment," Bedawi quoted the general as saying.
The warning was another sign of a "get tough" campaign against insurgents, who have accelerated attacks against U.S. and coalition forces in recent weeks. U.S. forces had eased off on raids and other offensive measures during the Islamic holy month of Ramadan, which began Oct. 27, to avoid offending religious sensitivities.
Hours after Abizaid's warning, U.S. jets dropped three 500-pound bombs in the Fallujah area late Saturday after three paratroopers from the 82nd Airborne Division were wounded in an ambush. There was no report of casualties from the bombing, which appeared aimed primarily at intimidating local residents.
"Neither America, nor the father of America, scares us," a local resident, Najih Latif Abbas, said. "Iraqi men are striking at Americans and they retaliate by terrifying our children."
In other developments:
The soldier killed Sunday was the 37th American service member to die in Iraq this month and the 151st killed in action since President declared an end to major combat May 1. One hundred others have died outside of combat. Since the war began, 389 Americans and 56 foreign troops have died.
U.S. officials have blamed supporters of Saddam Hussein and foreign fighters for the upsurge in violence. However, a U.S. officer in Saddam's hometown Tikrit said Monday that there were no signs that foreign Islamic radicals have gained a foothold there.
Lt. Col. Steve Russell, a battalion commander with the 4th Infantry Division, said gunmen killed or captured during recent attacks against coalition forces were Saddam loyalists and "we have yet to kill or capture a foreign fighter in Tikrit."
Meanwhile, tensions between U.S. forces and Iraqis in the Shiite Muslim enclave Sadr City rose Monday after the head of the U.S.-appointed municipal council, Muhanad al-Kaadi, was shot dead by an American soldier guarding the municipal headquarters.
The U.S. military said the shooting occurred when the driver of a car which was blocked from entering the building's courtyard attacked one of the guards, allegedly trying to grab his weapon. Another soldier shot the man and he later died in hospital, the statement said.
Al-Kaadi, a youthful, fluent English speaker, had been trying to improve relations between the Americans and residents of the impoverished Shiite community.