Major General Sulayman Muhammad, who commanded a National Guard division in southern Iraq, was shot dead on Friday in the New Baghdad district of the capital. Two of his sons were wounded in the attack, the police said.
Two car bomb attacks over two days have killed 14 people and wounded 20 others, including two US soldiers, according to US and Iraqi officers.
In the deadlier of the two attacks, a bomber blew up his car on Thursday evening at a checkpoint in Ramadi, killing 11 Iraqi special police commandos and wounding 25 other people, according to the US military.
The blast wounded nine Iraqi security-force members, three civilians and two US soldiers, US Marine Captain Jeffrey Pool said.
The US 2nd Marine Division said the bomber blew himself up at a checkpoint in the east of the city, which is 110km west of Baghdad.
In the second attack, which took place on Friday in Iskandariya, a lawless area just south of Baghdad, a bomber blew up his car beside an Iraqi army convoy, killing three soldiers and wounding six, soldiers at the scene said.
Checkpoints were established at entrances to the city last month to try to crack down on anti-government fighters who have a strong presence there.
Also on Thursday evening, unidentified attackers killed five female translators working for the US military in an eastern Baghdad neighbourhood, police Captain Ahmad Abud said.
Iraqi soldiers and police officer face
constant peril in the line of duty
The translators "were heading home when gunmen driving two cars sprayed them with machine-gun fire", Abud said on Friday. Further details were not immediately available.
Fighters routinely target US forces and their perceived collaborators as well as members of Iraq's government and army and police forces.
The US military says better control must be gained of the strife-torn country before any major US troop withdrawal.
Meanwhile, Aljazeera has learned that an Iraqi National Assembly meeting scheduled for Saturday has been postponed.
However, talks are continuing between the United Iraqi Alliance and the Kurdish parties on distribution of seats in the presidential council and ministerial portfolios in a new Iraqi government.
For his part, interim Prime Minister Iyad Allawi has called for the negotiation process to be accelerated, in view of the fact that two months have elapsed since the holding of elections.