Baghdad, Iraq ? Iraq’s incoming prime minister struggled to find a Sunni Arab to run the key Defense Ministry in time to join Iraq’s first democratically elected government when it takes office today. A torrent of bloodshed — at least 140 killed in five days — followed the approval of a Cabinet that mostly shut out members of the disaffected Sunni minority.

Disputes persisted over the Defense Ministry on Monday after Prime Minister-designate Ibrahim al-Jaafari filled six of the seven Cabinet seats left undecided last week, said al-Jaafari aide Laith Kuba. The defense portfolio — in charge of some 70,000 soldiers and national guardsmen — is destined for a Sunni, part of an attempt to balance the conflicting demands of Iraq’s many religious and ethnic factions.

Iraqi police, fire fighters and bystanders gather at the scene after a car bomb exploded in the Karadah district of Baghdad, Iraq, Monday, killing at least three and injuring many others, according to local police.

At least 23 Iraqis were killed Monday, including eight soldiers cut down by a suicide attacker who blew up a truck at a checkpoint south of the capital, and six civilians caught in a car bombing that set fire to a Baghdad apartment building. A British soldier also was killed by a roadside bomb in the southern city of Amarah.

In New York, U.N. Secretary-General Kofi Annan issued a statement strongly condemning the “cruel and heartless” violence apparently aimed at undermining Iraq’s newly formed government.

The skyrocketing attacks are blamed on an insurgency believed largely made up of members of Iraq’s Sunni minority, who dominated for decades under Saddam Hussein but were excluded from meaningful positions in a partial new Cabinet announced Thursday.

Al-Jaafari had promised to form a government that would win over Sunni moderates and reduce Sunni support for the insurgency. He offered them six ministries and a deputy premiership, but only four ministers have been approved so far by the National Assembly.

His initial choice for defense minister, the most important ministry destined for a Sunni, Saadon al-Dulaimi, was rejected by members of his Shiite-dominated alliance because of suspected ties to Saddam’s Baath Party, which brutally repressed the majority Shiites and Kurds. Since then, rival Sunni factions have submitted a number of candidates for the job. Three Sunni lawmakers quit al-Jaafari’s alliance, complaining he should look within his own coalition first to fill Cabinet posts.

Al-Jaafari wants to have all positions finalized before the new government is sworn in today, Kuba said. He declined to identify those already selected before they are presented to the interim National Assembly for approval.