Shelling in the Iraqi city of Fallujah, held by anti-government fighters for more than four months, has killed 11 people in less than 24 hours, a doctor said on Sunday.

It was not immediately clear who was behind the shelling in various areas in the south of city, just a short drive to the west of Baghdad.

The bombardment began on Saturday night and continued into Sunday, Doctor Ahmed Shami said, adding that four people were also wounded.

In a sign of both the reach of anti-government militants and the weakness of security forces, all of Fallujah and shifting parts of Anbar provincial capital Ramadi, farther west, have been out of government control since early January.

The crisis in the desert province of Anbar, which shares a long border with conflict-hit Syria, erupted in late December when security forces dismantled Iraq's main Sunni Arab anti-government protest camp just outside Ramadi.

Militants subsequently seized parts of Ramadi and all of Fallujah, the first time anti-government forces have exercised such open control in major cities since the peak of the deadly violence that followed the US-led invasion of 2003.

The bloodshed comes during vote counting from the April 30 general election, the first since American troops withdrew in late 2011, and amid a protracted surge in nationwide unrest.

While officials are quick to blame external factors for the violence, analysts and diplomats say widespread anger among the Sunni Arab minority is also a key cause.