The first blast came from an explosives-laden car left in a parking lot in Karrada, a busy commercial area home to several government offices, as well as courts and a hospital. The explosion killed four civilians and three police officers and wounded 21, a police officer said.
A few minutes later, a suicide bomber with an explosives belt blew himself up at the main gate of an office affiliated with the Higher Education Ministry, killing two police officers and two civilians, the police officer said. The attack wounded 12, he said.
Meanwhile, police said gunmen stormed the house of an anti-al-Qaeda Sunni fighter in the town of Youssifiyah, killing the Sunni fighter along with his wife, son, sister and a cousin. Youssifiyah is 20 kilometers south of Baghdad.
Insurgents frequently attack members of the Sunni militia, known also as Sahwa, which joined forces with US troops at the height of the Iraq war to fight al-Qaeda.
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Medical officials confirmed the casualty figures for the attacks. The officials spoke on condition of anonymity because they were not authorized to talk to journalists.
No one immediately claimed responsibility for today's attacks, which came two days after a series of car bombings rocked the capital and killed at least 34 people. That was the bloodiest day in Iraq since April 28, when militant strikes on polling stations and other targets killed 46.