Iraqi security forces cross a bridge built by soldiers over the Euphrates River as they advance towards Ramadi (AP)

A wave of attacks across Iraq has killed at least 15 civilians, as government forces press on with their offensive to dislodge Islamic State militants from a major city west of Baghdad.

In the Shiite-majority town of Khalis, about 50 miles 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 in the western city of Ramadi, 80 miles west of Baghdad, from IS extremists who control large swaths of land in western and northern Iraq and in neighbouring Syria.

The Iraqi security forces' advance was slowed on Wednesday by snipers, roadside bombs and booby-trapped buildings, military spokesman Brig Gen 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 two miles 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 on the northern and western perimeter.

"I think the fall of Ramadi is inevitable," Mr Warren said, though it cautioned it will take some time and "it's going to be a tough fight".

PA Media