A man was then killed when a mine went off on Palestine Street as a police patrol passed. Five people were wounded, three of them policemen.
Six people were wounded, three of them soldiers, when their convoy hit a makeshift mine.
Outside the capital, three people were killed and one wounded when armed men opened fire near the northern oil city of Kirkuk, police Lieutenant Abdullah al-Obeidi said.
Nationwide, levels of violence had reached a four-year low, but they have picked up again in recent weeks.
On Monday, 34 people were killed and dozens wounded, including 22 people when a woman suicide bomber blew herself up in a crowd of people who had gathered for a feast in the province of Diyala.
On Friday, a suicide bomber blew up a lorry near a police station in Dujail, north of Baghdad, killing 31 people in the deadliest attack in nearly three months.
General Raymond Odierno, the new commander of US forces in Iraq, , warned when he took up his new post on Tuesday that recent security gains remained "fragile and reversible".