Iraqi government forces pressed on Wednesday with their offensive to dislodge Islamic State militants from the major city of Ramadi as a wave of attacks across the country killed at least 15 civilians, officials said.

No one immediately claimed responsibility for the attacks, though they bore the hallmarks of ISIS. The Sunni militant group has targeted Iraqi forces, civilians and especially Shiites.

The attacks came as Iraqi government forces shifted their concentration to the last district held by ISIS militants in Ramadi, located about 80 miles west of Baghdad.

"In the coming days will be announced the good news of the complete liberation of Ramadi," Iraqia TV quoted Army Chief of Staff Lt. General Othman al-Ghanemi as saying, according to Reuters.

Iraqi state TV said Wednesday that government troops have killed hundreds of militants, but did not say how many of its own forces died.

The Iraqi military's advance was slowed Wednesday by snipers, roadside bombs and booby-trapped buildings, military spokesman Brig. Gen. Yahya Rasool told The Associated Press. Rasool said some of the families that were trapped in Ramadi had managed to flee the city and reached safe areas.

Iraqi security forces reported progress Tuesday in recapturing some areas in the city.

In May, the Iraqi government suffered a major blow when ISIS militants took over Ramadi, the capital of sprawling western Anbar province and Iraq's Sunni heartland. It was the government's biggest defeat since ISIS 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 neighborhoods, less than 2 miles from the city center, said Gen. Ismail al-Mahallawi, the head of operations in Anbar province. The Iraqi air force and the U.S.-led international coalition were providing air support to troops on ground and bombing ISIS targets, he said.

Hours after Iraqi government announced the gains, Col. Steve Warren, a spokesman for the U.S. military in Baghdad, 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," Warren told Pentagon reporters, cautioning that it will take some time. "It's going to be a tough fight."

Since overrunning Ramadi, the Islamic State group has destroyed all the bridges around the city. It also demolished the Anbar operations command and fanned out into the city's residential areas to set up less conspicuous centers of command.

Meanwhile, in the Shiite-majority town of Khalis, about 50 miles north of the Iraqi capital, two explosives-laden cars were detonated Wednesday. The first car was parked inside a bus station and that explosion killed three and wounded 10, a police officer told The Associated Press.

The second car bomb exploded at the town's outdoor grocery market, killing four civilians and wounding eight.

In and around Baghdad, five bombs went off in commercial areas, killing eight civilians and wounding 35, two police officers said. Three medical officials confirmed the casualty figures. All officials spoke on condition of anonymity as they were not authorized to release information.

The Associated Press contributed to this report.