At least 51 people have been killed and 139 injured by a wave of bomb blasts across Iraq's capital of Baghdad.

Eleven car bombs went off in markets and car parks across the city in a fresh wave of deadly attacks that bore the hallmark of the affiliated terror group of Islamic State of Iraq (Isis).

The bombs were detonated during morning rush hour and targeted mostly Shiites neighbourhoods.

The deadliest blast hit a vegetable market in eastern Sadr City, killing seven people and wounding 16, officials said.

Bombs claimed lives also in the Shiite neighbourhoods of New Baghdad, Habibiya, Sabaa al-Bour, Kazimiyah, Shaab, Ur, Shula as well as the Sunni neighborhoods of Jamiaa and Ghazaliyah.

There was no immediate claim of responsibility but the interior ministry blamed Isis.

"Our war with terrorism goes on," ministry spokesman Saad Maan said. "Part of the problem is the political infighting and regional conflicts. There are shortcomings and we need to develop our capabilities mainly in the intelligence-gathering efforts."

Ethnic violence is rife in the country and has reached its worst levels in recent years, with more than 4,000 people killed during the past few months, and more than 5,000 since January, according to United Nations data.

Isis has increased attacks against Iraq's Shiite-led government, fuelling an outbreak of sectarian violence that threatens to push the country into civil war, as it did in 2006 and 2007.

The al-Qaida spinoff has carried out a spate of terrorist attacks and staged spectacular prison breaks. It has killed more people in Iraq in the last few months than at any time since 2008 and extended its reach into neighbouring Syria, where it has exploited the civil war to take control of large rebel-held areas.

Two Christian churches were recently stormed by Isis fighters in Syria's northern town of ar-Raqqah, where the group is believed to have abducted Jesuit priest Paolo Dall'Oglio.