The operation started on Thursday and is ongoing. It involves Iraqi police and soldiers, backed by US troops, going through residential areas to capture militiamen and illegal weapons.
The region has become a centre for arms smuggling and the crackdown on militias is also aimed at ending the widespread illegal movement of cude oil in southern Iraq.
Many militias allegedly gain their funds from the smuggling of crude oil.
However, some analysts say the crackdown has been employed to weaken the movement of Muqtada al-Sadr, the Shia leader, who is a rival to Nuri al-Maliki, the Iraqi prime minister.
Amara, a city of 350,000 people, has huge numbers of people living in abject poverty and has long served as a key centre for support of al-Sadr's anti-US stance and conservative Islamic politics.