Nuri al-Maliki, Iraq's prime minister, has promised the crackdown will cover "every inch" of Iraq if opponents of his government don't accept his "olive branch of peace".
He also announced an expansion of the Iraqi army - with plans to encourage a return of officers who served under Saddam Hussein.
Maliki said: "The higher command has made the decision to bring back the officers from various ranks to the Iraqi Army in accordance to its needs and capabilities.
"And for those who do not wish to come back, they should be honoured and receive their rights including pensions, salaries and their skills can be utilized in other public institutions and administrations throughout the state."
Sadr City control
Sadr City is thought of as firmly in the hands of the al-Madhi Army, a group led by Muqtada al-Sadr, a Shia leader.
Caldwell said that US officials had spoken daily with community leaders in Sadr City in preparation for the operation.
He said: "There is no problem between the two sides, and we are trying to set up a small security centre there."
US military were thought to be converting the al-Jazair police station in Sadr City into a joint operations centre.
Police said there had been US military activity at the police station since Friday.
US troops, assisted by Iraqi forces, also moved through the Jamila area on the northern edge of Sadr City and sealed off some streets, police said.
Falah Hassan, a spokesman for Sadr's bloc in parliament, said there was "no reason" for such a "provocative act".
He said: "We understood that Iraqi forces only would conduct the search, and if that they faced resistance then US forces could intervene. But that was not the case with today's operation."
Also on Sunday, US troops arrested three people and wounded a female bystander in a raid on a mosque in Baghdad, a military spokesman said.
It has been unusual for US soldiers to enter Iraqi mosques. In most cases, Iraqi security forces search places of worship while US forces remain outside.
"Coalition force's soldiers respect the sanctity and holiness of all places of worship," said lieutenant colonel Chris Garver, a US spokesman.
He said the raid had been carried out because a "suspected terrorist" was known to be inside.
Three people were arrested in the raid.
"Mosque entries occur only as a last resort, and only when substantial and credible evidence shows insurgent activity is occurring there," said Garver.
During the operation an Iraqi woman was wounded in the thigh and head, a US military statement said.
Elsewhere in Baghdad, an Iraqi journalist was shot dead outside his home in a Sunni neighbourhood on Sunday.
Mohan al-Dhaher, a senior editor at the independent al-Mashriq daily newspaper, had just left his house to go to work when armed men in two vehicles pulled up and tried to kidnap him, neighbours and colleagues said.
Al-Dhaher, who was married with four children, was shot dead by the when he tried to resist, neighbours said.
The body of another local journalist, Jamal al-Zubeidi, editor-in-chief of the al-Safeer newspaper, was found last week in a Shia area of Baghdad, a local journalists' association said.
It said al-Zubeidi was kidnapped on February 24 from central Baghdad.
In other violence, seven Iraqi policemen were killed in a car bomb attack in al-Baghdadi district outside of Baghdad, an Iraqi security source said.
|Maliki said he would unveil his cabinet |
reshuffle "either this week or next" [EPA]
Meanwhile, Maliki said on Sunday that he will undertake a cabinet reshuffle within the next two weeks.
Maliki said the changes to the cabinet would be unveiled "either this week or next".
Maliki has promised a shake-up of his 39-member multi-party cabinet for several months, calling in November for a "comprehensive" reshuffle "to send a message to all ministers that they may be replaced if they don't succeed".
Shia officials have said Maliki's government could collapse if US-backed Baghdad security plan fails to put a brake on sectarian violence.