A wave of bombings targeting commercial areas in and around Iraq's capital Baghdad has killed at least 18 civilians, according to officials.

The deadliest attack on Sunday took place in Baghdad's Khilani Square, where a car bomb killed at least seven people and wounded 25 others, a police officer said. The car was parked near a Sunni mosque and a gathering of motorcycle vendors.

Hours earlier, an explosives-laden car exploded in the town of Mahmudiya, about 30km south of Baghdad, killing at least four civilians, another police officer said.

Three people were killed and 13 wounded in another car bomb explosion in Baghdad's southwestern Amil neighbourhood, the officer added, while two others were killed in a blast in the nearby Bayaa district.

In the capital's eastern suburb of Husseiniyah, a bomb went off in an outdoor market, killing two civilians and wounding six others, police said.

Medical officials confirmed the toll, and all officials spoke to the Associated Press news agency on condition of anonymity.

The Islamic State of Iraq and the Levant (ISIL) group and other Sunni groups are believed to be behind the attacks.

The blasts came as Iraqi security forces continued to clash with ISIL fighters for control of territory in Iraq's Western Anbar province.

In an interview with state TV, interior ministry spokesman, Brigadier General Saad Maan Ibrahim, said government forces were close to recapturing the town of Garma, just east of the ISIL-held city of Fallujah, 65km west of the capital.

Ibrahim added that fighting was also ongoing to dislodge the fighters from the canal lock system near Lake Tharthar just to the north.

ISIL forces attacked the area on Friday, killing a senior officer and around a dozen other soldiers and officers.