The attacks come as security forces and allied Shiite militiamen and Sunni tribesmen fight to regain ground from militants led by the Islamic State (IS) jihadist group who overran swathes of the country in June.
The blast in the Karrada area of Baghdad killed at least eight people and wounded more than 20, while eight died and 13 were wounded in central Kirkuk.
The day before, a suicide bombing, car bomb and shelling struck Shiite-majority areas of northern Baghdad, killing at least 28 people and wounding more than 60.
In addition to the blasts and shelling, two more suicide bombers were arrested near the base before they could attack, officials said.
Sunni extremists often target members of Iraq's Shiite majority, whom they consider heretics, and also frequently attack security forces.
The United States has carried out a more than five-week air campaign against the IS jihadists, while France has announced it will take part in strikes on them in Iraq as well.
