Gunmen detonated suicide vests inside a shopping complex in Baghdad on Monday and a car bomb exploded nearby in an attack claimed by Islamic State that killed at least 18 people and wounded 40 others.

Two bombs later went off in the eastern town of Muqdadiya, killing at least 23 people and wounding another 51, security and medical sources said. Another blast in a southeastern Baghdad suburb killed seven more.

Islamic State militants controlling swathes of Iraq's north and west claimed responsibility for the attacks in Muqdadiya and at the Baghdad mall, which it said had targeted a gathering of "rejectionists", its derogatory term for Shi'ite Muslims.

The Iraqi government last month claimed victory against the hardline Sunni militants in the western city of Ramadi, and has slowly pushed them back in other areas.

A security official in Anbar province on Monday said ground advances backed by US-led coalition air strikes killed about two dozen insurgents and pushed others out of areas near the government-held city of Haditha in Iraq's northwest.

Monday's bombings left the biggest death toll in three months. Interior Ministry spokesman Brigadier General Saad Maan blamed "this terrorist group after they suffered heavy losses by the security forces", without naming Islamic State.

Seven people, including two policemen, were killed in the car bomb blast near the Jawaher mall in the predominantly Shi'ite district of Baghdad Jadida, police and medical sources said.

Five more people were shot dead by the gunmen storming the mall, and six others were killed when those same assailants detonated their explosive vests, the sources said.

"People started running into the shops to hide, but (the militants) followed them in and opened fire without mercy," said Hani Fikrat Abdel Hussein, a shop-owner standing amid shattered glass and rubble at the site of the blasts.

Police regained control of the shopping complex, in the east of the city, and a senior security official told state television there were no hostages, rejecting reports that people had been held.

"The security forces are at the scene and managed to recover the wounded. The situation is under control," Maan added.

As well as the violence meted out by Islamic State, Iraq is also gripped by a sectarian conflict mostly between Shi'ites and Sunnis that has been exacerbated by the rise of the militant group.

At least seven people were killed when a suicide bomber driving a car attacked a commercial street in a southeastern Baghdad suburb on Monday, police and medical sources said.

The blast in the Sunni district of Nahrawan left more than 15 people wounded, the sources added.

Earlier in the day, three people were killed and eight others wounded when a car bomb claimed by Islamic State went off near a restaurant in Baquba, 65 km northeast of Baghdad, security and medical sources said.

Two bombs later exploded in an area frequented by Shi'ite militia fighters in the town of Muqdadiya, another 15 km further northeast, security sources said.

At least 23 people were killed and 51 wounded in those blasts. A bomber detonated his suicide vest inside a casino in the town. A car bomb parked outside then went off as medics and civilians gathered at the site of the first blast.

Security officials said they had imposed a curfew for all of Diyala province, where Muqdadiya and Baquba are located.

Parliamentary speaker Salim al-Jabouri, who is from Muqdadiya, said he was in contact with security and political leaders there and warned violence there aimed to "undermine efforts for civil peace", state TV said in a news flash.

There was no immediate claim of responsibility for the attack in the Baghdad suburb.-Reuters