Shortly after the bombings hit, the extremist Islamic State, which has been behind recent deadly attacks in Baghdad and beyond, claimed responsibility for two of the attacks, both in the Iraqi capital.

Such assaults are seen as an attempt by the militants to distract the security forces' attention away from the front lines.

The attacks came amid a key Iraqi military operation to dislodge IS militants and retake the city of Fallujah, west of Baghdad, which has been in IS hands for over two years.

The operation was launched a week ago, with Iraqi forces teaming up with paramilitary troops and backed by aerial support from the US-led coalition.

The deadliest of today's attacks took place in the northern, Shiite-dominated Shaab neighbourhood of Baghdad where a suicide bomber rammed his explosives-laden car into a checkpoint next to a commercial area, killing eight civilians and three soldiers.

The explosion also wounded up to 14 people, a police officer said.

A suicide car bomber struck an outdoor market in the town of Tarmiyah, about 50 kilometers (31 miles) north of Baghdad, killing four civilians and two policemen, another police officer said, adding that 19 people were wounded in that bombing.

And in Baghdad's eastern Shiite Sadr City district, a bomb motorcycle went off at a market, killing three and wounding 10, police said. Medical officials confirmed casualty figures.

All officials spoke on condition of anonymity as they were not authorised to release information.

In an online statement, IS claimed responsibility for the attacks in Shaab and Sadr City, saying they targeted members of Shiite militias. The Associated Press could not verify the authenticity of the statement but it was posted on a militant website commonly used by extremists.

Fallujah is one of the last major IS strongholds in western Iraq. The extremist group still controls territory in the country's north and west, as well as Mosul, Iraq's second largest city.

Yesterday, Iraqi Maj Dhia Thamir said troops have recaptured 80 per cent of the territory around Fallujah since the operation began and are currently battling IS to the northeast as they seek to tighten the siege ahead of a planned final push into the city center.

In a televised speech yesterday to parliament, Iraqi Prime Minister Haider al-Abadi called on Fallujah residents to either leave the city or stay indoors.

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