Iraqi and US troops have set up additional checkpoints in Baghdad
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The Iraqi prime minister says there has been a reduction in sectarian killings and kidnappings since a Baghdad security plan was launched 10 days ago.
Nouri Maliki says 426 suspected militants have been held and almost the same number killed since 14 February.
On Saturday, at least seven people were killed and more than 30 injured in a series of attacks in the Iraqi capital.
Separately, the Iraqi interior ministry said Iraqi and US troops killed dozens of Sunni militants north of Baghdad.
'Willing co-operation'
After visiting the command centre co-ordinating the joint Iraqi-US security operation in Baghdad, Mr Maliki said 426 militants had been detained and "around that number" had been killed.
He said many more militants had left the capital and vowed to bring them to justice.
Mr Maliki stressed that the new plan - which had seen thousands of extra US and Iraqi troops sent to Baghdad - also depended on the co-operation of the people.
He said the indications were that Iraqis were willingly co-operating.
US military commanders have also spoken positively about the operation.
But they have said that the rebels are currently laying now, warning that higher levels of violence to will probably return.
Despite Mr Maliki's optimistic words, at least seven people were killed in Baghdad in a number of bombings and mortar attacks, the BBC's Jane Peel says.
'Dozens killed'
North of Baghdad, Iraqi soldiers - backed by US aircraft - raided a Sunni rebel base early on Saturday, Iraqi Interior Ministry spokesman Brig Abdul-Kareem Khalaf said.
He said dozens of suspected members of the Islamic Army in Iraq had been killed during the operation that lasted several hours.
The spokesman said he was unaware of any civilian deaths.
The US military said it had no report about the operation, the Associated Press news agency reported.