BAGHDAD - At least 72 people were killed and more than 140 wounded by three bombings in Baghdad on Tuesday, police and medical sources said, extending the deadliest spate of attacks in the Iraqi capital so far this year.

Islamic State claimed one suicide bombing which killed 38 people and wounded over 70 in a marketplace in the northern district of al-Shaab.

A car bomb in nearby Sadr City killed at least 28 dead and 57 wounded, and another car blew up in the mixed Shia-Sunni neighbourhood of al-Rasheed, south of the capital, killing six and wounding 21, the sources said.

Prime Minister Haider al-Abadi ordered the arrest of the security official in charge of al-Shaab's security after the attack, Abadi's office said in a statement, without giving a reason for the detention.

Attacks claimed by IS in and around the city last week killed more than 100 people, the highest death toll in so few days so far this year, sparking anger and street protests over the government's failure to ensure security.

Security had improved in Baghdad in recent years as sectarian tensions waned and the city's perimeter was fortified. Islamic State, the ultra-hardline militants who control parts of north and west Iraq, have not tried to take the capital but carry out increasingly regular suicide bombings there, hitting Shia areas and government targets.

With the latest death tolls, fears are growing that Baghdad could relapse into the bloodletting of a decade ago when sectarian-motivated suicide bombings killed scores of people every week.

This has cranked up pressure on Abadi who is struggling to solve a political crisis or risk losing control of parts of Baghdad to Islamic State militants. Away from the capital, Iraq's military is waging a counter offensive against the group.

Abadi has said the crisis, sparked by his attempt to reshuffle the cabinet in an anti-corruption bid, is hampering the fight against Islamic State and creating space for more insurgent attacks on the civilian population.

A spokesman for the Baghdad Operations Command told state television the attacker in al-Shaab had detonated an explosives-filled vest along with a planted bomb. Initial investigations revealed that the bomber was a woman, he said.

Islamic State said in a statement distributed online by supporters that one of its fighters had targeted militiamen with hand grenade and a suicide vest. There were no immediate claims of responsibility for the other two bombings.

Meanwhile, an Australian working for a land mine clearance charity was killed in northern Iraq on Tuesday while trying to defuse a bomb planted by Islamic State militants, three of his colleagues said.

The man was working under the non-profit Swiss Foundation for Mine Action (FSD) in the Daquq area, around 200 km north of Baghdad. Islamic State were driven out of Daquq last year but left behind hundreds of improvised explosive devices.

FSD programme manager Alex Van Roy said when the man was killed instantly when the bomb containing up to 7 kilograms of explosives blew up.

He said the family of the victim had asked that his name be withheld.

FSD has removed some 500 homemade bombs in the Daquq area since it began working there around two months ago, Kurdish FSD team member Aso Sabah al-Din said.

The team of two dozen includes both expatriates and Kurdish forces who control the area and who say they do not have the capabilities to deal with the bombs left by Islamic State.