Police said the first attack took place when a suicide bomber rammed his explosive-laden car into the checkpoint in Baghdad's northern district of Shulla, killing three police officers and six civilians. Officials said the blast wounded at least 22 people.
Later on, another suicide car bomber attacked a police base in Garma east of the city of Fallujah in Anbar province, killing nine police officers and wounding 10, authorities said.
Two police officials said the bomber in the attack used an Iraqi army vehicle seized earlier by Islamic State group, though no group immediately claimed either attack.
Baghdad and outlying areas see near-daily bombings. Many of them are later claimed by the Islamic State group, which seized large parts of the country during a stunning blitz last year. Iraqi security forces have been struggling to recapture areas lost to the militants ever since.
