Polish military spokesman Capt. Andrzej Wiatrowski said the raid in Karbala, 50 miles south of Baghdad, took place before dawn. An undetermined quantity of weapons and ammunition were seized.
U.S. officials said only that the targets were "criminal elements" in the city, where an American lieutenant colonel and two other U.S. soldiers were killed last week.
Tensions rose in Karbala last week after a transport official seized a bus owned by followers of radical cleric Muqtada al-Sadr and held him in the al-Mukayam mosque, where one of al-Sadr's offices are located. That led to clashes between rival Shiite groups in which and several people were killed or injured.
In other developments:
The confrontation at the Oil Ministry illustrated the cultural chasm that divides the U.S. occupation from ordinary Iraqis. It began when 28-year-old Amal Karim showed up for work Tuesday morning and faced a routine search at the ministry entrance by U.S. soldiers.
When the Americans told her to submit her bag to a sniff-search by a dog, she refused, saying the bag held a copy of the Quran, Iraqi witnesses later reported.
Devout Iraqis often carry Islam's holy book with them, and Muslims consider dogs to be dirty, disease-spreading animals.
"When she refused, the American soldiers took the Quran out of her bag and threw it to the ground," said one woman, Zaineb Rahim. "Then the American soldiers handcuffed Amal."
Pushing and punching followed between soldiers and Iraqis, Americans struck out with rifle butts, and soon about 100 Iraqis had gathered in angry protest outside the huge, modern building on Baghdad's northern edge, leading the Americans to fire shots in the air, the witnesses said.
As the protesters hoisted an Iraqi flag, officers of the tiny, newly formed Iraqi army appeared, trying to ease tensions. Karim was eventually released and was summoned to the oil minister's office, colleagues reported.
The incident Monday in Fallujah began when insurgents attacked a dismounted patrol from the 82nd Airborne Division with a homemade bomb and small-arms fire.
Reporters and Iraqi witnesses said the paratroopers raked the area with return fire, then raided a mosque and houses looking for the attackers. They detained at least nine Iraqis, including a woman, residents said.
The Associated Press saw that one of the civilians killed, Iraqi Nazem Baji, had a gunshot wound in the back of his head and his hands were tied in front of him with plastic bands similar to those used by the U.S. military when they arrest suspects.
The victim's brother said he had been told by witnesses that the Americans bound and executed Baji. The U.S. military press office in Baghdad said it had no information on the allegation.