Bombings in a Shiite-majority area of Baghdad and other attacks killed 37 people on Thursday, as Prime Minister Nuri al-Maliki accused neighbouring states of backing jihadists in Iraq.

The government has failed to curb a year-long surge in violence that has reached levels not seen since 2008, when the country was just emerging from a brutal period of sectarian killings in which tens of thousands died.

In the deadliest attack on Thursday, an explosives-rigged motorcycle ripped through an area of motorcycle shops in the Shiite-majority Sadr City district of Baghdad, killing at least 27 people and wounding 40, the interior ministry said.

And a car bomb in Sadr City killed at least one person and wounded five, officials said.

Sunni extremists frequently target members of Iraq's Shiite majority, who they consider apostates.

The capital is hit by near-daily bombings and shootings, including periodic coordinated vehicle bomb attacks that leave dozens of people dead.

In Mishahada, north of Baghdad, a car bomb exploded near an army patrol, killing at least two soldiers and wounding three.

Other attacks hit areas in northern Iraq.

A roadside bomb exploded near a Sahwa anti-Al-Qaeda militia patrol in the Sharqat area, killing two fighters and wounding four, while a roadside bomb near a police station in Tuz Khurmatu killed two people and wounded 15.

And three soldiers died in clashes with militants in Kirkuk province.

The latest violence came as Maliki accused foreign states of backing a powerful jihadist group, the Islamic State of Iraq and the Levant in Iraq.

"Some states do not want ISIL, especially on their territory, but they want ISIL in Iraq" for "sectarian" reasons, Maliki said in an interview broadcast on Iraqiya state television.

"We know the details of ISIL and its foreign ties and the ties of states to it, and the funding that comes to it," Maliki said.

The premier was apparently referring to Sunni-majority Gulf states including Saudi Arabia, Iraq's neighbour to the south.

Militants in Iraq have been bolstered by widespread discontent among members of the country's Sunni Arab minority, who say they are marginalised and unfairly targeted with heavy-handed security measures, and by the bloody civil war in neighbouring Syria.

In a sign of the reach of militants and the weakness of security forces, the city of Fallujah -- just a short drive from Baghdad -- and shifting parts of Anbar provincial capital Ramadi, to its west, have been held by anti-government fighters since early January.

Maliki said in the interview that except for Fallujah, Anbar province was under government control, though militants in fact hold areas outside the city.

Of the situation in Fallujah, he said: "God willing, it will end soon."

Nationwide, violence has killed more than 710 people since the beginning of the month, and over 1,700 so far this year, according to AFP figures based on security and medical sources.