In Baghdad, officials said police found three bodies of women with gunshots to their head in northeastern neighborhood of Ur. Police said they are investigating the incident.
And in the northern city of Mosul, a roadside bomb struck an army patrol, killing one, authorities said.
Two medical officials confirmed the soldier's death and the Baqouba casualties. All officials spoke on condition of anonymity because they were not authorized to speak to the media.
Violence has spiked in Iraq since April, with the pace of killing reaching levels unseen since 2008. Thursday's attacks bring the death toll across the country so far this this month to 607, according to an Associated Press count.
Speaking Thursday in Washington, Iraqi Prime Minister Nouri al-Maliki warned that terrorists "got a second chance" to thrive in Iraq, largely as the result of the rise of al-Qaida fighters in neighboring Syria's civil war. He said the world needs to help Iraq deal with its deadly insurgency.