The surge in unrest comes as the country grapples with a prolonged political deadlock and months of protests by the Sunni Arab community alleging discrimination at the hands of the Shiite-led authorities.
Analysts warn that the political stand-off could persist until general elections due next year.
In Abu Ghraib, just west of Baghdad, a bomb in a market killed three people and wounded at least 10 others, while in nearby Garma, gunmen opened fire on a group of policemen and killed three before fleeing.
In the main northern city of Mosul, meanwhile, three civilians were gunned down in an electronics shop.
Separate attacks in Taji, Sharqat and Mosul -- all predominantly Sunni Arab towns and cities north of Baghdad -- left one person dead and 13 others wounded.
Among the victims were one Sahwa fighter killed and five wounded, a day after a wave of attacks targeting the militiamen killed at least eight.
The Sahwa are a collection of Sunni tribal militias who turned against Al-Qaeda and joined forces with the US military from late-2006 onwards, helping to turn the tide of Iraq's bloody insurgency.
They are often targeted by Al-Qaeda-linked militants who regard them as traitors.
The latest attacks pushed the overall nationwide death toll for June to 428, the third successive month the figure has topped 400, according to an AFP tally based on reports from security and medical officials.
April and May saw more than 1,000 people killed in all.
However, figures compiled by the United Nations are higher still, pegging the death toll for April and May at more than 1,750.
Iraq has seen a rise in violence since the beginning of the year, coinciding with rallies among the Sunni Arab minority against what demonstrators see as discrimination and the authorities targeting them.
Analysts say a government failure to address protesters' grievances has given militant groups recruitment fodder and room to manoeuvre.