Prime Minister-designate Nouri al-Maliki, left and Iraqi President Jalal Talabani chat during farewell lunch for outgoing Iraqi Prime Minister Ibrahim al-Jaafari

Iraq's national security adviser says he expects the country's prime minister designate to name a new cabinet within days, not weeks.

Iraqi Prime Minister-designate Nouri al-Maliki has until May 21 to submit a cabinet to the Iraqi parliament for approval. But the country's National Security Adviser Mowaffak al-Rubaie says an announcement could come sooner than that.

"I do not think we are talking about weeks. I think we are talking about a few days," he said.

The Iraqi official told CNN's Late Edition Maliki is putting the final touches on his cabinet, which he said will include what he described as "strong" and "meaningful" representation from Iraq's Sunni community.

Although the Sunnis only make up about 40 percent of Iraq's population, they dominated the country under Saddam Hussein. But, following his overthrow, and the resurgence of the country's 60 percent Shia population, Sunni political participation has been under question.

"Everybody is going to be represented in this national unity government, and this is going to last for another four years," added al-Rubaie. "And the top priorities for this national unity government is security, economy, stimulation of economy and also, providing services to our people."

Meanwhile, the Iraqi national security adviser rejected suggestions that the country should be split into three sections, run by Iraq's three dominant ethnic and religious groups - the Shias, the Sunnis and the Kurds. He said there can be greater autonomy on the local level for some things, but that overall, the country should remain unified.

"We need to build a new 'Iraqism', a new national identity for Iraq," he commented. "This is a new Iraq based on a democratic, parliamentary, constitutional system, federal system. It has to be completely decentralized, and give the decentralized regions to run their own affairs, with exception of defense and foreign affairs and few other things."

In northern Iraq, the autonomous region of Kurdistan formally unified its two local governments.

Meanwhile, car bombs in Baghdad and the Shi'ite holy city of Karbala killed at least 11 people. The U.S. military in Iraq says the blast in Karbala killed two, which is fewer than earlier reported.

Also, in Baghdad, police found the bullet-riddled bodies of 42 men.