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A leader in Iraq's powerful Hashd al-Shaabi Shia militias has put forward a plan to secure the so-called "belt areas" of Baghdad, following another deadly attack in the capital.

Leader of the Asaib Ahl al-Haq (League of the Righteous) militia, Safaa al-Saadi, told local media on Tuesday that authorities in Baghdad have failed to come up with a "clear plan" to eliminate Islamic State group [IS] "sleeper cells" from the area.

On Tuesday, a car bomb claimed by IS struck the Karrada district of Baghdad, killing at least 20 civilians in the latest of a string of deadly attacks, targeting civilians.

"We have a plan and if the the government agrees it will be possible to get rid of the IS cells," Saadi said, according to °®Âþµº's Baghdad correspondent.

"The Hashd al-Shaabi factions have a deep understanding of all areas. We have the ability to gather information and then take action with precision."

Security measures, including road blocks, have been implemented in the bustling commercial area of Karrada since a deadly blast killed more than 300 people in the Shia-majority district in July.

	The July Karrada bombing killed over 300 people [Getty]

In recent months, IS militants have turned to insurgency-style attacks in public areas far from the front lines after Iraqi government forces and allied militias pushed the extremists out of many areas they had captured in western and northern Iraq during a mid-2014 blitz.

Tribal leader, Sheikh Abdallah al-Zobai, however, told °®Âþµº that handing over full control of the Baghdad belt to the militias would result in an increase of violations against local residents.

The Shia militias have been accused of committing serious abuses and reprisal attacks against Sunnis thought to belong or to be sympathetic to IS in cities recently retaken from the jihadists.

"The Hashd al-Shaabi militias have been continuously present in the belt, where they have carried out violations in plain sight of the security forces who no longer have any control over them," the local elder in Abu Ghraib city said.

"The militias are trying to dominate security in the area so they can be the sole force on the ground without oversight or regulations."

This week, parliament member for the Sunni-dominated Union of Nationalist Forces, Liqaa al-Wardi said that incidents of killings, kidnappings and looting carried out by militiamen have been on the rise in the Baghdad belt.