Tough new security measures have been put in place in Baghdad in an effort to win back control of the city's streets.
The new security plan is the toughest since the invasion of 2003
Some 40,000 Iraqi and US troops were put on the streets just after dawn, a day after President Bush flew into Baghdad and met PM Nouri Maliki.
Mr Maliki later said he was willing to talk to some insurgents, as long as they did not have blood on their hands.
Meanwhile violence continued, with clashes breaking out between gunmen and security forces in the city's north.
40,000 troops on the streets, extra checkpoints, more night raids and air strikes
Ban on personal weapons
Overnight curfew extended to begin at 2030
Vehicle ban during Friday afternoon prayers
Special uniforms and badges for all security personnel
Hotline for anonymous tip-offs
No casualties were reported in the clashes, in the mainly Sunni Adhamiya district, which officials said lasted about half an hour.
A car bomb also exploded in northern Baghdad, killing at least two people and injuring 10, police said. A second car bomb exploded in another northern area, but no-one died.
Fears are high that al-Qaeda in Iraq is preparing new attacks after the killing of their leader Abu Musab al-Zarqawi.
Zarqawi's successor, named as Abu Hamza al-Mujahid, has reportedly vowed to defeat "crusaders and Shias" in Iraq.
But Mr Maliki said that although he would not negotiate with killers of innocent people, dialogue was possible with some rebel groups.
"The national reconciliation initiative holds the possibility of having dialogues with rebels who are opposed to the political process and want to rejoin it with guarantees," he said.
"If their hands are not stained with blood we will open the door to them for a dialogue."
The new security measures will be the strictest imposed on Baghdad since the US-led invasion in 2003.
The nightly evening curfew will now begin at 2030, not 2300 as it did before, and run until 0600 the next morning.
Extra troops were posted throughout Baghdad early on Wednesday, setting up new checkpoints to secure road travel in and around the city.
Residents said they had already noticed the difference, with more vehicles being stopped and searched and long queues building up as a result.
But the BBC's Hugh Sykes in Baghdad says checkpoints and patrols provide easy targets for car bombers, and ordering a suicide car bomber to pull over could prompt him to detonate, thereby helping him to achieve his objective.
Insurgents are to be targeted by snap raids, with the majority of resources deployed to the most dangerous areas of Baghdad.
Officials sounded optimistic about the changes: "The terrorists cannot face such power," said Gen Mahdi al-Gharrawi, head of the interior ministry forces.
But the question among Iraqis is whether this is just a show of force or whether it can make a dent in the daily bombings and shootings that claim at least 20 to 30 lives in the capital every day.
Mr Bush's surprise visit to Baghdad on Tuesday gave Mr Maliki just five minutes' warning that the US president was in town.
The US president had been chairing talks in the US on future policy in Iraq and had been due to speak to Mr Maliki via videophone.
Instead Mr Bush personally congratulated him on the appointment of ministers in the Iraqi government for defence, security and the interior.