Police officials told the AFP news agency that two civilians were killed in the Sheikomar checkpoint blasts.
The two other victims were said to be members of the anti-al-Qaeda Awakening movement, also known as Sahwa, who are frequently targeted by anti-government fighters for siding with US forces.
Many Awakening members are former fighters who battled against US and Iraqi forces in the immediate aftermath of the US invasion of Iraq and the toppling of Saddam Hussein, the former Iraqi president.
A suicide car bomb that targeted an Iraqi police car on the road to Baghdad International Airport killed six people, including three police officers, on Wednesday.
US officials say that attacks in Baghdad are averaging about four a day, reportedly down nearly 90 per cent from levels in late 2006, when Shia-Sunni violence was at its high point and just prior to the America's so-called "troop surge".
But the number of attacks have increased in the last week, with a string of daily bombings in the capital that that have killed more than 30 people and wounded around 80 others.