Three Iraqi soldiers were killed on Monday in a double roadside bombing in the Ghazaliyah neighbourhood in western Baghdad, a police official said.
Fifteen others, including 11 civilians, were wounded in the attack.
In southern Iraq, a bus bomb killed at least six people, while in the northern city of Mosul two policemen were killed and two others wounded when a roadside bomb hit their patrol, two security officials said.
The US military on Monday freed another 35 members of a group linked to the abduction of five British citizens from Iraq's finance ministry in 2007, a representative for the group said.
The prisoner release means nearly 100 members of Asaib Ahl al-Haq, or League of the Righteous group, have left US custody since late last week.
In total, about 250 members have been freed since July as talks intensify over the fate of the sole British hostage believed to be still alive.
Salam al-Maliki, a representative of the group, said the talks were to seek the release of its leader, Sheikh Qais al-Khazali.
A group of armed men seized Peter Moore, a computer expert working for a US-based consultancy firm, and his four bodyguards in May 2007.
The bodies of at least three of the hostages have been identified, but Moore is believed to be still alive.