More than 20 people were killed and at least 50 were wounded in three bombings, including two suicide attacks, in Baghdad on Monday, said police and medical sources. According to the Guardian, DAESH has claimed responsibility for the suicide attacks.
The attacks came as Iraqi forces and Shiite militias are fighting DAESH in Falluja, their stronghold just west of the capital.
At least 12 people were killed and more than 20 were wounded when a car bomb blew up in the northern district of Shaab district.
Eight were killed and 21 wounded when a suicide bomber detonated a car packed with explosives near a government building and a police station in Tarmiya, a predominantly Sunni suburb north of Baghdad.
Another suicide bomber riding a motorbike set off his explosive belt in Sadr City, a popular Shiite district in Baghdad, killing three and injuring nine.
Falluja became the first Iraqi city to fall to DAESH in January 2014, and the terror organisation subsequently overran vast areas in northern and western Iraq.
It is the second largest city under DAESH control after Mosul.
On Monday, army units moved to the southern entrance of Falluja, "steadily advancing" under air cover from the US-led coalition, according to a military statement read on state TV.
Iraqi Army launched its operation to retake Falluja on May 23, first by tightening a six-month-old siege around the city 50 kilometres (30 miles) west of Baghdad.
The offensive is causing alarm among international aid organisations over the humanitarian situation in the city, where more than 50,000 civilians remain trapped with limited access to water, food and health care.