Car bomb attacks in Baghdad and the Iraqi province of Diyala, mostly claimed by the Islamic State jihadist group, have killed at least 30 people, police and medical sources said Wednesday.

The deadliest of the attacks was in the Iraqi capital's eastern district of Baghdad al-Jadida, a predominantly Shia area that has been one of the most targeted by car bombs in recent years.

At least 19 people were killed and 43 wounded when a car bomb exploded near a market there on Tuesday, a police colonel and hospital sources said.

Another four people were killed and 10 wounded in a similar attack in the southern neighbourhood of Zafaraniya.

The Islamic State (IS) group claimed responsibility for both attacks, saying they had targeted Shia militiamen, a claim it often makes even when most of the victims are civilians.

A car bomb also struck a joint police and army checkpoint in Tarmiya, a town which lies on of the main highways north of Baghdad, police said.

At least three members of the security forces were killed and nine wounded.

Also on Tuesday, a car bomb went off in Mandali, a town in the eastern province of Diyala which lies near the border with Iran, killing at least four people.

A huge suicide car bomb attack claimed by IS killed dozens of people in Khan Bani Saad, a town just north of Baghdad, on Friday.

Baghdad announced in January that Iraqi forces had "liberated" Diyala, significant parts of which had been overrun by IS after the jihadists launched a brutally effective offensive in June 2014.

The jihadists no longer have fixed positions in the province but have reverted to their old tactics of planting car bombs and carrying out suicide operations or hit-and-run attacks.