Four car bomb attacks and a mortar strike on Shia muslim parts of Baghdad killed 36 people and wounded 98 within the space of two hours this afternoon, police and medical officials said.

An Iraqi Shia political figure said the assaults, part of a surge of violence in Shia neighbourhoods in recent weeks, were revenge attacks by Sunni militants Islamic State.

A suicide car bomb hit an army checkpoint near a restaurant in the northern district of Talbiya at 2.30pm (11.30am Irish time), killing nine people, said officials.

A pair of car bombs exploded in the district of al-Dawlai in western Baghdad 45 minutes later, killing 16 people and wounding 35.

Minutes after that, five mortar rounds hit the neighbouring Shia district of al-Shaoula, killing another five and wounding 21 others.

A car bomb then exploded in the nearby Hurriya district, leaving six dead and wounding 14 others.

"They [Islamic State] are making a statement to the Shias fighting them... We can target you in your household," said Kareem al-Noori, from the Badr Organisation, a powerful Shia political party with a militia wing.

There was a relative lull in violence in Baghdad after IS swept the city of Mosul and much of northern Iraq in June and threatened to march on Iraq's capital.

However, the violence has increased in the city since late September.

Prime Minister Haider al-Abadi, in office for a month and still without a defence or interior minister due to rifts among the country's main Shia and Sunni political parties, yesterday sought to soothe Baghdad's jangled nerves.

"Baghdad is safe and the vicious terrorists can't and will not reach it," Mr Abadi said in a televised speech at a military ceremony.

"Our brave security forces have managed to secure Baghdad and its perimeter."