BAGHDAD (REUTERS) - 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 in Iraq and Syria (ISIS) claimed one suicide bombing which killed 38 people and wounded over 70 in a marketplace in the northern, mainly Shi'ite Muslim district of al-Shaab.

A car bomb in nearby Shi'ite Sadr City killed at least 28 dead and 57 wounded, and another car blew up in the mixed Shi'ite-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 ISIS 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.

ISIS, the ultra-hardline Sunni 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 Shi'ite 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 ISIS 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 ISIS 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.

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