The attacks came as Iraqi Kurdish militias, backed by US airstrikes, seized the town of Sinjar from the Islamic State group in a major blow to the extremists.
Following its blitz last year, the IS which splintered off from Iraq's al-Qaida branch now holds about a third of Iraq and neighboring Syria in its self-declared caliphate.
The suicide bomber struck a memorial service held for a Shiite militia fighter killed in battle against IS in the Iraqi capital's southwestern suburb of Hay al-Amal, a police official told The Associated Press. That explosion killed 21 people and wounded at least 46, he said.
Also Friday in Baghdad, a roadside bomb detonated at a Shiite shrine in Sadr City, killing at least five people and wounding 15, police officials said. Hospital officials confirmed the casualty figures. All officials spoke on condition of anonymity as they were not authorized to talk to reporters.
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Since the emergence of IS extremists, Baghdad has seen near-daily attacks, with roadside bombs, suicide blasts and assassinations targeting Iraqi forces and government officials, with significant casualties among the civilian population.
The violence has killed hundreds and displaced tens of thousands of Iraqis.
The militias, which later formed an umbrella paramilitary force called the Popular Mobilization Forces, have been an integral part in the battle against the Islamic State group, supporting Iraqi forces in battles in Salahuddin, Anbar and Baghdad provinces.
In a statement distributed on pro-IS Twitter accounts, the Sunni militant group said the aim of Friday's attacks was "revenge for our monotheist brothers in al-Fallujah, al-Anbar, and Salahaldin," referring to ongoing Iraqi military operations to retrieve land lost to the IS in those locations.