A suicide driver has rammed his explosive-laden car into a police checkpoint in Baghdad, killing 31 people, including more than a dozen civilians, en route to a Shia shrine.

Police and hospital officials told the AP news agency that at least 13 civilians had been killed in the blast and 58 were injured.

The Islamic State on Wednesday claimed responsibility for the attack, one of the deadliest in a recent string of bombings in the capital.

IS has claimed responsibility for a wave of bombings in Baghdad, including several on Saturday which killed 27 people.

The attack occurred at the entrance to Baghdad's Khazimiyah district, where many cars were heading to the Imam Al-Khadim Shrine in the lead up to the Eid feast commemorating the end of Ramadan, officials said on condition of anonymity.

Earlier on Tuesday, two mortar rounds landed near a police station in Baghdad's Sabi al-Bore neighbourhood, killing three policemen and wounding four others, a police officer said.

Meanwhile, in Fallujah, Iraqi government airstrikes killed 19 people, including several children, a health official told the Reuters news agency.

The Iraqi army has been shelling the city, west of Baghdad, for months, trying to drive out Sunni fighters from the IS. The group, formerly known as ISIS, overran the city in January backed by discontented local Sunni tribal leaders.

Ahmed al-Shami, a spokesman for the Fallujah health office, said the 19 dead included women and children and that the local hospital had also received 38 wounded since Monday evening.

Residents of Fallujah and the nearby town of Garma said helicopters fired artillery and dropped three barrel bombs on the city and two on Garma.

Prime Minister Nouri al-Maliki's office said on Tuesday that he had met Sunni tribal leaders from several provinces where the conflict is raging.