BAGHDAD - The Islamic State (IS) group on Sunday claimed responsibility for the suicide car bomb attack in Iraqi capital Baghdad that killed at least 79 people and wounded 133 others, the group said in an online statement.

One of the group's suicide bombers, nicknamed Abu Maha al-Iraqi, detonated his car bomb at a crowd of Shiite people in the predominantly Shiite district of Karrada-Dakhil in southern central Baghdad, according to the statement, of which the authenticity could not be independently verified.

Earlier in the day, an Interior Ministry source said that two busy commercial areas in Bagdad were hit by car bombings, with one of the attacks occurring at about 1:00 a.m. local time (2200 GMT) when a suicide bomber detonated his car bomb at a crowded thoroughfare in Karrada-Dakhil district.

The powerful blast set fire to five nearby buildings and several shops and destroyed many stalls and civilian cars at the scene which was crowded with shoppers who are preparing their families for Eid al-Fitr, or the Festival of Fast-breaking, which marks the end of a month-long of fasting for Muslims, said the source.

The Iraqi capital was the scene of another attack after midnight when a booby-trapped car went off at Shallal popular market in Baghdad's northeastern district of Shaab, killing a civilian and wounding five others, the source added.

Iraqi Prime Minister Haider al-Abadi visited the scene of the massive suicide car bomb attack in Karrada Sunday morning, and promised to punish those behind the attacks, according to a statement issued by his office.

"The terrorist groups carried out such desperate deadly attack as a result of being crushed in the battlefield," the statement said, referring to the latest defeat of the IS in the country's western province of Anbar, including its stronghold in Fallujah, some 50 km west of Baghdad.

Abadi also sent his condolences to the families of the killed and the wounded people and promised that "victory over these terrorist groups is very close."

The IS has frequently targeted the security forces and areas where crowds of people gather, including markets, cafes and mosques across Iraq.

Iraq has been hit by a new wave of violence since the IS terrorist group seized parts of Iraq's northern and western regions in June 2014.

Earlier, a report by UN Assistance Mission for Iraq (UNAMI) estimated that 662 Iraqis were killed and 1,457 others wounded in acts of terrorism, violence and armed conflict in June across Iraq.