At least 125 people have been killed and over 180 injured in two bombings that hit crowded market areas in Baghdad on Saturday night, in the deadliest single attack in the Iraqi capital this year.

A refrigerator truck packed with explosives blew up outside a restaurant in Karrada, a busy shopping area in Baghdad packed with families as they celebrated Ramadan.

Sorry, this video has expired Deadly blasts rock Baghdad, IS claims responsibility

Footage taken of the scene the morning after the explosion showed a large blast area, with dozens of blackened, mangled cars and at least four buildings severely damaged or partly collapsed.

Shortly after the Karrada attack, another explosion went off in eastern Baghdad, killing at least five people.

Iraqi Prime Minister Haider al-Abadi ordered changes to Baghdad security measures in response to the bombing.

He visited the site of the attack on Sunday and vowed "punishment" for the perpetrators, according to his office, which later announced three days of mourning for the victims.

A video posted on social media showed men apparently angry at the Government's failure to prevent the carnage throwing rocks at what was said to be Mr Abadi's convoy.

In another video, a bystander could also be heard cursing at the Prime Minister.

Mr Abadi struck a conciliatory tone over anger directed towards him.

"I understand the emotional feelings and actions that occurred in a moment of sadness and anger," he said in a statement.

People gather at the site of the suicide car bomb in the Karrada shopping area in Baghdad. ( Reuters: Khalid al Mousily )

Bombing claimed by IS after fall of Fallujah

The Islamic State group (IS) issued a statement claiming the Karrada suicide bombing, saying it was carried out by an Iraqi as part of the group's "ongoing security operations".

The jihadist group said the bombing targeted members of Iraq's Shiite Muslim majority, whom it considers heretics and frequently attacks in Baghdad and elsewhere.

The bombing came a week after Iraqi forces completely recaptured Fallujah, a city 50 kilometres west of Baghdad that was a key IS stronghold.

Violence in the capital has decreased since IS overran large areas north and west of Baghdad in 2014, but the jihadists have previously stepped up attacks following military losses.

With Fallujah retaken by Baghdad, second city Mosul is the only major Iraqi population centre held by IS.

ABC/AFP