The troops moved into parts of the city without encountering resistance
Iraqi security forces have been fanning out in the southern city of Amara, as part of a crackdown on Shia militias and criminal gangs.
Among those arrested is Amara's mayor, Rafi Abdul Jabbar, who is a supporter of the Shia cleric Moqtada Sadr.
The Sadr office in Amara has accused the Iraqi forces of targeting his group, and ignoring government orders to detain only wanted men.
The Iraqi authorities say troops have recovered a number of weapons.
Correspondents say there has been no shooting so far. A number of armed men avoided arrest by throwing their weapons into the street or canals.
It is the latest attempt by the Iraqi government to impose its control in the south of the country, where Shia groups are engaged in a power struggle.
A similar offensive in Basra in March led to weeks of fighting in which hundreds of people died.
Police have imposed curfews in certain areas, but said government offices, schools and colleges would not be affected.
The operation, which is backed by US forces, has been called Promise of Peace and a government statement said it would "impose law... and confront outlaws".
"We are glad they are bringing stability to the city," said one resident, quoted by Reuters news agency, as the police were searching his house.
British troops handed control of the 250,000-inhabitant city to Iraqi forces in April 2007, but security has remained fragile and militia activity intense.
Amara is a stronghold for the Sadrist Mehdi Army militia, but is also said to be a haven for arms smugglers between Iraq and Iran, which is not far from the city.
Sadrist officials have said they support the attempt to restore authority to the city, and would not put up resistance.
But the arrest of Mr Abdul Jabbar provoke a rebuke from his officials based in the important Shia religious centre of Najaf
"We were surprised by the violations and the random raids. We condemn the latest events that show a deliberate targeting of Sadr's movement," said Hazim al-Araji in Najaf.
Mr Abdul Jabbar "was very cooperative and working to make the plan a success," Mr Araji said.