At the government's historic first meeting on Wednesday, the newly appointed prime minister, Iyad Allawi, flagged security as the "number one priority".
He spoke on the same day as a Baghdad blast struck the mainly Sunni Muslim area of Adhamiyah, killing at least four and wounding 34 others, according to a medical official.
Women were seen screaming and wailing at the hospital as ambulances ferried the wounded to the emergency department. Police said at least five children were among the injured.
In what later appeared to be a botched car bombing in the nearby Harthiyah neighbourhood, one person was killed and another wounded when the vehicle exploded, police officer Salah Hasan said.
The force of the explosion scattered body parts up to 30 metres from the wreckage.
The blasts came as a two-month-old conflict between the militia of Muqtada al-Sadr and US forces raged on in Iraq's Shia heartland.
"A complete national reconciliation is essential for building a new Iraq. This means rearranging the social fabric and restoring its balance away from score-settling and through direct, free and honest elections"
Iraqi interim president
Six Iraqis were killed in Kufa, one in its twin city of Najaf, and two in the Baghdad Shia neighbourhood of Sadr City, medical sources and officials from al-Sadr's office said.
The latest wave of deadly violence marked the collapse of an attempt to impose a 72-hour truce announced on Tuesday by the Najaf governor.
Security will be the main challenge of the new Iraqi Cabinet, which is responsible for paving the way to free elections next year.
Allawi, a former Baath dissident who had close ties with the US Central Intelligence Agency, was chosen partly for his security credentials.
"Yesterday and today, there have been terrorist attacks and, as Iraqis, we want to work with the multinational force and with friends and our brothers in the region to defeat these continued threats," he said at the cabinet meeting.
For his part, freshly appointed president Ghazi al-Yawir said he wanted to lay the foundations for a new Iraq based on reconciliation, in a newspaper interview to be published on Thursday.
"A complete national reconciliation is essential for building a new Iraq," al-Yawir told Al-Mada.
"This means rearranging the social fabric and restoring its balance away from score-settling and through direct, free and honest elections."
Security Council scene
A new draft of a UN resolution due to spell out the level of sovereignty which the Iraqi government will enjoy, has been put together by the United States and Britain.
If passed, the resolution would give the Iraqi government control over the army and the police.
The conflict in the Shia heartland
shows no signs of ending
It also offers a rough date for the departure of occupation troops, saying the occupation's mandate would expire "upon completion of the political process" to create a constitutionally elected Iraqi government.
The country's first free elections are due in January 2005 but a constitution could be adopted as late as 2006.
But Allawi left little doubt at the cabinet meeting that the force, even under the UN flag, would still be under firm US control.