The US military said the attack at the entrance to the Green Zone in central Baghdad killed two Iraqi army members and three civilians.
In the third attack, a roadside bomb targeted a police patrol near Technology University in eastern Baghdad, killing two civilians and wounding four other people.
And in Baquba, 60km northeast of Baghdad, a policeman was killed when a roadside bomb blew up near his car, police said.
The rush hour violence came as Iraqi legislators prepared for a vote later in the week on a security agreement with Washington that would allow US forces to remain in the country for up to three more years.
Iraq's cabinet approved the deal more than a week ago, after nearly a year of negotiations, but it has drawn criticism from some who want US troops to leave sooner.
The Iraqi government has urged parliament to approve the pact, which would govern the more than 150,000 US troops deployed in over 400 bases across Iraq when their current UN mandate expires at the end of the year.