A suicide bombing left 28 people dead in a Baghdad market Sunday, local broadcaster Alsumaria reported, citing police officials.
Another 62 people were injured in the attack in the mainly Shiite Sadr City district in eastern Baghdad, the report says.
Alsumaria quoted a police official as saying that the bomber, who was riding a motorcycle, blew himself up outside mobile phone shops in the market.
A statement posted online in the name of the Islamic State extremist organization claimed responsibility for the attack.
The statement, which dpa could not independently verify but which was consistent with previous such claims by the jihadist group, said the attack had been carried out by two suicide bombers.
Earlier, residents in the Abu Ghraib area on Baghdad's western outskirts reported an attack by Islamic State on an army barracks in the area.
The militants also seized control of a grain store in the area, the residents said.
The Baghdad operations command said security forces had fought off an attack by Islamic State west of the capital and killed two would-be suicide bombers.
The attacks come weeks after Iraqi security forces cleared Islamic State fighters out of the city of Ramadi, the capital of western Anbar province.
On Saturday, General Hadi Arzij, head of the Anbar police, revealed that 15 bomb disposal experts have been killed during efforts to defuse booby traps left behind in the city by the jihadists.
Iraqi Prime Minister Haider al-Abadi has vowed to eliminate Islamic State from the country this year, although observers say that any attempt to recapture the country's second-largest city, Mosul, from the jihadists will be difficult.