Maliki late last year negotiated the support he needed for form a unity government after nearly nine months of political gridlock following March parliamentary elections. Many ministers are serving in an interim capacity while lawmakers wrangle over the final touches on a new government.
The new government includes 42 Cabinet posts and 12 ministers of state. Iraqiya, which narrowly won the March contest, is expected to take control of a new National Council for Strategic Policies.
Shaker Kattab, a spokesman for Iraqiya, told the Voices of Iraq news agency Monday that Maliki and Allawi are expected to discuss the makeup of the new council during meetings this week.
"The (council) will be a high-level Iraqi institution, similar to the presidency, Council of Ministers and the Parliament," he was quoted as saying.
Meanwhile, at least 13 people were killed Monday when a car bomb exploded near a bush station filled with Shiite pilgrims in the holy city of Karbala. The explosion marks an uptick in violence in Iraq. Allawi last week criticized the government for not doing enough on security matters.
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