Police sources said the suicide bombers were riding motorcycles and blew themselves up in a crowded mobile phone market in Sadr City, wounding more than 100 people in addition to the dead.
A Reuters witness saw pools of blood on the ground with slippers, shoes and mobile phones at the site of the blasts, which was sealed off to prevent further attacks.
Islamic State suicide bomber kills six outside Shia mosque in Baghdad
In a statement circulated online, Islamic State said it was responsible for the blasts: "Our swords will not cease to cut off the heads of the rejectionist polytheists, wherever they are," it said, using derogatory terms for Shia Muslims.
Iraqi forces backed by airstrikes from a US-led coalition have driven Islamic State back in the western Anbar province recently and are preparing for an offensive to retake the northern city of Mosul.
But the militants are still able to strike outside territory they control, often targeting members of Iraq's Shia majority, most recently on Thursday when two Islamic State suicide bombers killed 15 people at a mosque in the capital.
Prime Minister Haider al-Abadi said the attacks were in response to Islamic State's recent defeats, "This gang targeted civilians after it lost the initiative and its dregs fled the battlefield before our proud fighters," he said on his official Facebook page.
At dawn on Sunday, suicide bombers and gunmen attacked Iraqi security forces in Abu Ghraib, seizing positions in a grain silo and a cemetery, and killing at least 17 members of the security forces, officials said.
Security officials blamed Islamic State, and a news agency that supports the group said it had launched a "wide attack" in Abu Ghraib, 25 km (15 miles) from the center of Baghdad and next to the international airport.
Footage circulated online by the Amaq news agency appeared to show Islamic State fighters crouching behind dirt berms and launching the attack with automatic rifles, machine guns and rocket-propelled grenades. Reuters could not verify the video's authenticity.
Security forces had mostly regained control by Sunday evening but officials said there were still clashes.
Baghdad-based security analyst Jasim al-Bahadli said the assault suggested it was premature to declare that Islamic State was losing the initiative in Iraq.
"Government forces must do a better job repelling attacks launched by Daesh. What happened today could be a setback for the security forces," he said, using an Arabic acronym for Islamic State.
COUNTER OFFENSIVE
Army and police sources said the militants had attacked from the nearby Islamic State-controlled areas of Garma and Falluja, driving Humvees and pickup trucks fixed with machine guns.
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A curfew was imposed as a regiment of Iraq's elite counter-terrorism forces was mobilised to retake the silo in Abu Ghraib and prevent the militants approaching the nearby airport, security officials said.
Iraqi army helicopters bombarded Islamic State positions in the and Interior Ministry spokesman Brigadier General Saad Maan said at least 20 militants had been killed in the government's counter offensive.
Fighters from the Hashid Shaabi, a coalition of mainly Iranian-backed Shia militias, were mobilised to Abu Ghraib to reinforce regular government forces in the area, said Jawad al-Tulaibawi, a local Hashid commander.
Powerful Shia cleric Moqtada al-Sadr also called on fighters loyal to him to be on alert to protect Baghdad. Shia militias like Sadr's 'Peace Brigades' were seen as a bulwark against Islamic State's sweeping advance in 2014 which threatened Iraq's capital and its most sacred Shia shrines.
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