In the Shi’ite-majority town of Khalis, about 80km north of the Iraqi capital, two explosives-laden cars were detonated.
The first car was parked inside a bus station and that explosion killed three and wounded 10, while the second car bomb ignited at the town’s outdoor market and left four civilians dead and eight injured.
In and around Baghdad, five bombs went off in commercial areas, killing eight civilians and leaving 35 people injured.
No-one immediately claimed responsibility for the attacks, though they bore the hallmarks of IS.
They came a day after Iraqi security forces reported progress in recapturing some areas of Ramadi, 130km west of Baghdad, from IS extremists.
The Iraqi security forces’ advance was slowed yesterday by snipers, roadside bombs and booby-trapped buildings, military spokesman Brigadier General Yahya Rasool said.
He added that some of the families that were trapped in Ramadi had managed to flee the city and reach safe areas.
In May, the Iraqi government suffered a major blow when IS militants took over Ramadi, the capital of sprawling western Anbar province and Iraq’s Sunni heartland.
It was the government’s biggest defeat since IS swept through areas in the country’s north and west, including Iraq’s second-largest city of Mosul, in the summer of 2014.
On Tuesday, Iraqi counter-terrorism forces pushed into the Dubbat and Aramil neighbourhoods, about 3km from the city centre.
The Iraqi air force and the international coalition were providing air support to troops on the ground and bombing IS targets.
Hours after the Iraqi government announced the gains, US military spokesman in Baghdad Col Steve Warren said there were 250 to 350 Islamic State fighters in Ramadi, as well as several hundred outside the city.
“I think the fall of Ramadi is inevitable,” Warren said, though it cautioned it will take some time and “it’s going to be a tough fight”.
Meanwhile, the French government has promised a constitutional change to revoke the citizenship of dual-national terrorism convicts, as part of measures upholding the state of emergency imposed after the November 13 attacks in Paris.
Prime Minister Manuel Valls has also left open the possibility of prolonging the state of emergency beyond its current three-month window.