BAGHDAD, Nov 3 (Reuters) - Iraqi police backed by U.S. Marines arrested three bodyguards working for the mayor of Falluja and five other people after they came under attack from a government building on Friday, the U.S. military said. Falluja is in the restive western province of Anbar where U.S. forces are battling Sunni Arab insurgents. The U.S. military said a rocket-propelled grenade was fired at a joint Iraqi-U.S. coordination centre in Falluja and the Marines were then attacked by gunmen firing from a mosque. "A grenade was subsequently hurled at the Marines from a government building near the mosque, so the Iraqi police, with the Marines in support, gained entry to the structure and uncovered multiple AK-47s, ammunition and magazines," the military said in a statement. "Iraqi police officers detained eight Iraqi local nationals, including three of the Fallujah mayor's personal security officers, for suspected insurgent activity," it said, adding that seven of the detainees worked at the government centre. Falluja, 50 km (30 miles) west of Baghdad, has long been a thorn in the side of U.S. forces. In 2004, thousands of U.S. troops laid siege to the city on two occasions to crush insurgent rebellions. Four Marines were killed in combat on Thursday in Anbar, the military said on Friday.