The army said on Saturday that about 600 US Marines and Iraqi soldiers were participating in a major counter operation near Falluja.
Operation Scimitar started on Thursday with targeted raids in the village of Zaidan, 30km southeast of Falluja.
So far, 22 suspected fighters have been detained.
The US army said it did not announce the new military offensive earlier because commanders did not want to tip off fighters that a major operation had begun.
The offensive – named after a curved Asian sword – includes 500 Marines from the 3rd Reconnaissance Battalion, Regimental Combat Team-8, stationed in Okinawa, Japan, the military said.
About 100 Iraqi soldiers are supporting the operation, which the US says is designed to disrupt fighter activities in al-Anbar province.
The latest US offensive in the province came on the heels of Operations Spear, Dagger and Sword.
The heaviest fighting occurred during Operation Spear in mid-June in the town of Karabilah near the Syrian border.
The US said it had killed about 50 fighters in the last offensive which included air strikes, tank shelling and gun battles during Operation Spear. Parts of the city of Karabilah were left in rubble.
Exodus of diplomats
Meanwhile, Iraqi officials have become concerned about a possible exodus of diplomats from Baghdad after an al-Qaida website in Iraq claimed on Thursday that it had killed Egyptian envoy Ihab al-Sherif, who was seized by up to eight armed men on a street in western Baghdad last weekend.
Scimitar came after operations
A US commander acknowledged more needed to be done quickly to protect foreign diplomats.
Egyptian and Iraqi officials said Egypt would temporarily close its mission in Iraq and recall its staff – although al-Sherif’s body has not been found and the Web statement contained no evidence of his death.
Pakistan‘s Ambassador Mohammed Younis Khan left the country on Wednesday after his convoy was fired at in a kidnap attempt.
Bahrain‘s top envoy, Hassan Malallah al-Ansari, was expected to leave soon after he was slightly wounded in a separate attempt.