A prominent cleric, Shaikh Abd al-Alim al-Saadi, the provincial leader of the al-Anbar Scholars League and his son, Usama, were also detained, Aljazeera reported.
Spokesman for the influential Iraqi Muslim body, the Association of Muslim Scholars (AMS) in Ramadi, Shaikh Abd al-Fattah Muhammad, told Aljazeera that the US soldiers also raided the headquarters of the organisation.
In the raid on Aisha mosque, the US forces tore copies of the Quran and threw them on the ground, he said.
They stormed Shaikh Abd al-Jalil mosque and the Badia al-Samawat wal-Ardh mosque among others, the spokesman said.
US action has angered Muslims,
said AMS spokesman in Ramadi
The US action has angered Muslims who fear for their religion, honour and holy sites, Shaikh Abd al-Fattah Muhammad said.
There was no reason to arrest Shaikh al-Saadi, the spokesman said. He was in his mosque getting ready to perform prayers, he said.
"This is not the first shaikh the US forces have arrested," he said. "Many others have been detained before, such as Shaikh Uthman Mishaal, Shaikh Khalil Ata Allah and other imams, from inside their mosques by US forces," the AMS spokesman said.
Angry residents also accused US forces of breaking down doors and throwing around furniture inside the mosques.
The US military said the targeted mosques were suspected of "harbouring terrorists, storing illegal weapons caches, promoting violence and encouraging insurgent recruitment".
As marines and Iraqi forces combed the city, they exchanged fire with armed fighters, leaving two Iraqis dead and five wounded, hospital sources said.
"This is not the first shaikh the US forces have arrested"
Shaikh Abd al-Fattah Muhammad,
Iraqi forces were also part of the raid, the military said.
The Iraqi and US forces launched their raid at 4am (0100 GMT), hours after marines took fire from a mosque in the nearby town of Hiyt and called in an air strike on the building, the military said.
The raids followed two days of clashes in the city, 113km west of Baghdad.
Anti-US fighters fired two mortars at the city hall and neighbouring police directorate on Monday night, sparking gunfire and rocket-propelled grenade exchanges, residents said.
The raids follow two days of
clashes in the city
Loud explosions shook the city.
Three policemen and a civilian were killed, said Dr Dia Abd al-Karim at the city hospital.
Elsewhere, 11 members of the US-established Iraqi national guard have been killed and 10 others injured when armed men attacked the police headquarters in al-Karbala area, east of al-Qaim city, near the border with Syria.
Armed men in a car killed a local council member as he drove to work in the northern Iraqi city of Mosul on Tuesday, a local government spokesman said.
Abd al-Majid al-Antar was shot dead at about 9.30am (0630 GMT) in an eastern district of the city, 390km north of Baghdad. His bodyguards survived.