Police in Baghdad said a director in the Ministry of Culture and Housing was assassinated on Wednesday evening when unknown assailants attacked his car.
In Baghdad's Haifa Street neighbourhood, three members of the Kurdistan Democratic Party were killed in an ambush.
This was followed by clashes between Iraqi and US troops and an unknown number of fighters.
A US soldier was killed on Wednesday in an attack on his convoy north of the Iraqi capital near Balad, the US military said.
Two people were detained following the attack, which occurred some 70km north of the capital.
Meanwhile, the US military announced that the number of its troops in Iraq would be reduced, after an initial increase ahead of the 30 January elections.
US troops will be cut by roughly
13,000-19,000 to a pre-poll level
"We should be at pre-election levels in spring," Lieutenant General Lance Smith, deputy commander of the US Central Command in Iraq told reporters at the Pentagon.
Smith indicated that military personnel in Iraq would be cut by roughly 13,000 to 19,000 soldiers, to between 135,000 and 140,000, the level maintained before the the election.
Two brigades whose stay had been extended extra months for the polls would return to the US in March, he said.
The Portuguese government in Lisbon on Wednesday also announced that the country's 127-strong contingent of national guards would return home from southern Iraq on Thursday.
Lisbon will however keep four guards in Iraq to help provide training to Iraqi security forces, a spokesman for the force said.
The Portuguese contingent was
located in Nasiriya in the south
The national guards, a militarised police force, were deployed in the southern city of Nasiriya, where they served under Italian command, in November 2003 after major fighting in Iraq had ended.
In Paris, Foreign Minister Michel Barnier said France was doing all it could to secure the release of the journalist Florence Aubenas, who was kidnapped in Baghdad last month.
She has been missing since leaving a Baghdad hotel on 5 January in the company of her translator.
An Italian journalist Giuliana Sgrena was also seized in Baghdad last month.