The death toll from an attack on a Shiite shrine north of Baghdad has risen to 37, with 62 other people injured, Iraqi officials have said.

Police said the attack on the Sayyid Mohammed shrine in Balad, 80km north of the Iraqi capital, began with a volley of mortar fire on Thursday night, after which a suicide bomber targeted policemen at the entrance.

A second bomber entered the shrine with nine gunmen, targeting security forces as well as families gathering to celebrate Eid al-Fitr, the holiday marking the end of the holy month of Ramadan.

Police officials said a third bomber was killed before he detonated his explosives.

No group immediately claimed responsibility for the attack, which came as anger grew over a similar incident on Sunday in which at least 186 people were killed.

The massive truck bombing by the Islamic State group in Baghdad was the deadliest attack in Iraq since the 2003 US-led invasion and has stoked public unrest and spurred Iraqi officials to announce a number of new security measures.

Hospital officials and police said the death toll was now 186, but around 20 people are still missing, and more remains were being recovered from the rubble.

However, Ahmad Roudaini, from the health ministry's media office, said the death toll is 292.

The discrepancies in the numbers could not immediately be reconciled. Many of those killed have had to be identified with DNA-testing because their bodies were burned beyond recognition.

On Thursday evening, a crowd of angry friends and family members of the victims tried to push into one of the buildings hit in the truck bombing but civilian volunteers held them back.

The IS suicide bomber had detonated his explosives in Baghdad's central Karada neighbourhood, outside a shopping mall in a street crammed with people preparing for the Muslim holiday of Eid al-Fitr.

The area, packed with shops, cafes and restaurants, had swelled overnight with Baghdad residents eager from a respite from the daily fasting during the holy month of Ramadan.

Iraqi prime minister Haider al-Abadi later fired the commander of Baghdad's security operations as the embattled PM faces growing anger and protests over the lack of security in the capital.

The Baghdad bombing was one of the deadliest attacks since the US-led invasion of Iraq in 2003 and the deadliest single attack claimed by Islamic State worldwide.

After the Baghdad attack, Mr al-Abadi announced new security measures, but it is unclear if any of the measures have yet been implemented.

The minister of interior submitted his resignation on Tuesday, but Mr al-Abadi has not accepted it.

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