Muwaffaq al-Rubaie , the national security adviser, said on Saturday: "Very, very soon, we will have an agreement signed by the prime minister to hand over control of some cities.
"I very much hope it will happen before the elections."
The elections are to be on 15 December.
The transfer of some regions to Iraqi forces "undermine the claim by the terrorists that they are working against foreign troops", al-Rubaie said.
US forces have started handing over bases to Iraqi forces, most recently a complex of palaces built by former president Saddam Hussein on the outskirts of his home town near Tikrit.
Zalmay Khalilzad, the US ambassador to Iraq, indicated this month that America could start to pull out some of its 158,000 troops "beginning next year".
Meanwhile on Saturday, violence continued throughout the country.
Five people were killed and 16 wounded when a car bomber attacked a petrol station north of Baghdad, and a roadside bomb targeting a US military convoy exploded in a busy square in central Baghdad, wounding a US civilian contractor and four Iraqi nationals.
The Baghdad bomb targeted a
The car bomb explosion occurred at a station on a minor road running between Samarra and Duluiya.
The attack on the outskirts of Samarra, 125km north of Baghdad, devastated the petrol station and set a dozen cars ablaze, police and witnesses said.
It was not clear what the precise target of the bomber was.
US convoy targeted
The bomb targeting the US convoy damaged two civilian cars being escorted by the US military. Their occupants were evacuated to the military vehicles.
US Sergeant David Abrams declined to say whom the army was escorting, but said a US civilian contractor was lightly wounded.
Speaking to Aljazeera from Baghdad, Iraqi journalist Ziyad al-Samarrai said four Iraqis, two men and two women, and an unidentified number of foreigners were wounded in the morning explosion.
Witnesses and police sources confirmed that foreigners were travelling in the targeted civilian vehicles.
Al-Samarrai was unable to confirm whether there were any deaths caused by the explosion.
Also on Saturday, the US command announced that an American soldier from the 2nd Marine Division died when his vehicle was hit by a roadside bomb in western Iraq, near Hiyt, on Friday.
His death brings to at least 2112 the number of US military personnel killed in Iraq since the March 2003 invasion, based on Pentagon figures.
Basra imam killed
On Friday, the imam of a mosque in Basra was killed.
Four Iraqis and a US contractor
were injured in the Baghdad blast
The influential Association of Muslim Scholars (AMS) said the body of Shaikh Nadir Karim was found in the English cemetery
in Basra, southern Iraq
. He was the imam of al-Ashara al-Mubashara mosque.
The AMS said Karim was arrested by Iraqi intelligence officers from the Interior Ministry on Friday, and his body was discovered two hours later in the cemetery.Videotape on website
A videotape posted on a website allegedly by al-Qaida in Iraq
purportedly showed how the group planned and carried out the 24 October triple attacks on the Palestine
and Sheraton hotels in which 17 people were killed.
A narrator said the Palestine
hotel was occupied "by foreign journalists and security companies" but indicated that the Sheraton was the main target because it housed "assassination teams, intelligence groups" and American soldiers, according to an Associated Press report.
The authenticity of the videotape could not be verified.