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There was no immediate claim of responsibility, but most such attacks in Iraq are the work of the Islamic State jihadist group.
The bombing comes after Abadi’s government declared victory over IS in December and as the country gears up for parliamentary elections.
“Two suicide bombers blew themselves up in Tayyaran Square in central Baghdad,” said General Saad Maan, spokesman for the Joint Operations Command (JOC) which includes the army and police.
A police officer reported “31 dead and 94 wounded”.
Tayyaran Square is a bustling commercial centre and a place where day labourers gather in the early morning waiting for jobs. It has been the site of deadly attacks in the past.
Iraqi analyst Hisham al-Hashemi said attacks at the square since 2011 have killed 180 people, “often in the run-up to elections or just after the polls”.
They aim to “create chaos and exacerbate sectarian divisions”, he said.
Security forces cordoned off the scene of the blasts as ambulances gathered in the area, an AFP journalist said.
– May elections –
Abadi held an emergency meeting with the JOC and intelligence officials after the attack, his office said, asking them to “eliminate IS sleeper cells” and ensure the security of civilians.
Analysts have warned that IS would increasingly turn to such tactics as it was pushed underground after losing territory spanning the Iraq-Syria border.
Just hours after the first attack, another person was killed and three wounded in a grenade explosion east of Baghdad, the police said, blaming it on a tribal dispute.
Attacks increased in Baghdad after the start in 2016 of a battle to retake second city Mosul from IS. Iraqi forces retook the northern city in July last year.
In December, the government announced the “end of the war” against IS, which has been expelled from the Baghdad region and urban areas of Iraq that it controlled.
Jihadist elements are still active, however.
On Saturday, a suicide bomb attack near a security checkpoint killed at least five people in northern Baghdad.
And last November, IS claimed an attack by suicide bombers on a market on the outskirts of Baghdad that killed 11 people.
– Abadi, Hashed to stand separately –
The latest attacks come as Iraq gears up for elections in May, with voters deeply concerned about security in a country wracked by violence since the 2003 US-led invasion.
On Sunday, Abadi said he had persuaded the Hashed al-Shaabi paramilitary force which helped fight IS to join a “Victory Alliance” which he described as a “cross-sectarian” list.
But their alliance collapsed within 24 hours of being announced because of what a source close to the premier said was electoral reasons.
The collapse left Abadi’s list and the Hashed competing separately against the “State of Law” bloc of Nuri al-Maliki, his predecessor and a key rival who now holds the post of vice president.
Both Abadi and Maliki are members of the Shiite Dawa party.
Abadi was little known when he became premier three years ago, after Maliki ceded power to him in August 2014 amid IS’s sweeping offensive across the country.
Since taking over, Abadi has also rebuilt the armed forces and taken back disputed areas in the north from the Kurds, dashing their hopes for independence.
The Hashed, or Popular Mobilisation Units, for its part, is now seeking to become a key political player in Iraq after proving to be a formidable force on the battlefield.
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