More than 20 people were killed and about 50 injured in three bombings, including two suicide attacks, that hit Baghdad on Monday, police and medical sources said.The attacks came as Iraqi forces and Shi’ite militias are fighting Islamic State militants in Falluja, their stronghold just west of the capital.Twelve people were killed and more than 20 injured when a car bomb blew up in Baghdad’s northern Shaab Shi’ite district.Eight were killed and 21 wounded by a suicide bomber who 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 motorcycle set off his explosive belt in Sadr City, a popular Shi’ite district of Baghdad, killing three and injuring nine.There was no immediate claim for the blasts but the Islamic State group has claimed responsibility for nearly all such attacks in recent months.The latest was a suicide attack on Sunday in the town of Moqdadiyah, in Diyala province, northeast of Baghdad.IS released a statement naming the bomber, whose picture had been put up at checkpoints across Moqdadiyah after his mother tipped off the security forces but he was able to carry out the attack nonetheless.Under heavy pressure on the battlefield, the jihadist organisation has struck back with bloody attacks in Baghdad.The deadliest spate of bombings to hit the capital this year was earlier in May when three attacks on the same day, including a devastating blast in Sadr City, killed close to 100 people.Iraqi forces thrust into the city of Fallujah on Monday marking a new and perilous urban phase in a week-old operation to retake the IS bastion just 50 kilometres (30 miles) west of Baghdad.It is one of the last two major cities still held by the jihadists in Iraq, the other being Mosul, in the north.