The incidents happened one day after a series of blasts around the capital killed at least 32 people and injured more than 100 others.
Bombings and shootings have recently increased across the country.
Official figures show that July was the bloodiest month in Iraq in almost two years. The figures put the number of people killed in attacks in July at 325, the highest monthly death toll since August 2010.
At least seven people have been killed and 20 others injured in separate attacks across Iraq, according to security officials.
The series of attacks made Monday another bloody day for the long-suffering Iraqis.
In one of the incidents, a bombing left three civilians dead and two soldiers wounded in Mussayib, 60 kilometers (40 miles) south of Baghdad, First Lieutenant Mohammed al-Ammari said, AFP reported.
Another bomb attack in the Bayaa district of Baghdad killed at least three people and injured at least 18 more.
Meanwhile, in northern Iraq, gunmen shot dead district chief Abbas Najaf Agha in Kirkuk.