BAGHDAD -- A series of attacks targeting public places and Shiite militia checkpoints in and north of Iraq's capital killed 37 people Saturday, authorities said.

The first bombs exploded near the market in the town of Balad Ruz, 70 kilometres northeast of Baghdad, killing 11 people and wounding 50, police and hospital officials said.

Two suicide car bombers later attacked checkpoints manned by Shiite militiamen near the city of Samarra, killing 16 Shite fighters and wounding 31, authorities said.

Samarra and surrounding areas have been under constant attacks by the Islamic State group, which holds about a third of Iraq and neighbouring Syria in its self-declared caliphate. Clashes between Iraqi security forces and Islamic State militants followed the attack around Samarra, 95 kilometres north of Baghdad.

Saturday night, police said a bomb killed four people in western Baghdad, while another in Baghdad's neighbourhood of Abu Dashir killed three people and wounding eight.

Four mortar shells also hit homes in Sabaa al-Bour, just north of Baghdad, killing three people and wounding six, police said.

All officials spoke on condition of anonymity because they were not authorized to talk to journalists.

Iraq's Interior Ministry later said Iraqi border guards repelled an attack by Islamic State militants on a post on the Iraqi-Saudi border, saying several militants were killed.

Meanwhile in Baghdad, Iraqi Prime Minister Haider al-Abadi vowed to track down and punish those who smashed rare relics in the northern city of Mosul.

On Thursday, the Islamic State group released a video purportedly showing militants using sledgehammers to smash statues, describing them as idols. The vandalism drew global condemnation.

The destruction is part of a campaign by the extremists, who have destroyed a number of shrines. They are also believed to have sold ancient artifacts on the black market to finance their bloody campaign.

"Those barbaric, criminal terrorists are trying to destroy the heritage of the mankind and Iraq's civilization," al-Abadi said. "We will chase them in order to make them pay for every drop of blood shed in Iraq and for the destruction of Iraq's civilization."