A man looks at a burned police vehicle in Fallujah after clashes between Iraqi security forces and Al-Qaeda fighters. AP

A series of bomb blasts ripped through Shia neighborhoods of Baghdad on Sunday, killing at least 20 people. The attacks occurred as Iraq’s military attempted to drive Al-Qaeda fighters out of Sunni-dominated Anbar province, where clashes and airstrikes killed more than 40 people.

The deadliest of the attacks targeting Shias in Baghdad occurred when two parked cars laden with explosives detonated simultaneously near a restaurant and tea house. Officials said the blasts killed 10 people and wounded 26.

Authorities said another car bomb ripped through the capital's Shia eastern district of Sadr City, killing five and wounding 10. A fourth bombing killed three civilians and wounded six in a commercial area in the central Bab al-Muadham neighborhood, officials said. Two other bombings killed two civilians and wounded 13, police said.

The attacks in Baghdad came as Iraqi security forces continued to besiege two key cities in the country's western Anbar province after they were taken over by an armed group with links to Al-Qaeda called the Islamic State in Iraq and the Levant (ISIL).

The latest violence there has claimed dozens of lives. Twenty five ISIL members were killed in an air strike, according to the Iraqi military. Twenty two Iraqi soldiers and 12 civilians were also killed in clashes, with 58 wounded, according to Iraqi officials.

Clashes have been taking place since Monday in Anbar's provincial capital, Ramadi, and nearby Fallujah between Al-Qaeda fighters and pro-government Sunni tribesmen.

Ramadi was a stronghold of Sunni insurgents during the U.S.-led war. Al-Qaeda militants largely took both cities over last week and have been fending off incursions by government forces there since.

Earlier on Sunday, a senior Iraqi military commander said that it will take a few days to fully dislodge Al-Qaeda-linked fighters from the two cities.

Lt. Gen. Rasheed Fleih, who leads the Anbar Military Command, told state television Sunday that "two to three days" are needed to push the militants out of Fallujah and parts of Ramadi. Fleih added that pro-government Sunni tribes are leading the operations while the army is only offering aerial cover and logistics on the ground. He didn't elaborate on the operations.

"The quiet and safe life that is sought by the Anbaris will not be completely restored before a few hours or two to three days, God willing," Fleih said.