Clashes erupted between Iraqi troops and anti-government fighters on the outskirts of Fallujah on Saturday, as the militant-held city's main hospital said 366 people had been killed in the months-long conflict.

The latest unrest comes after security forces pressed an apparently unsuccessful assault into the city, which is west of Baghdad and has been out of government control since the beginning of the year.

Clashes on the city's northern fringes, in the region of Saqlawiya, broke out earlier on Saturday between Iraqi security forces and anti-government fighters, a tribal leader told AFP on condition of anonymity.

"With aerial cover, they tried to enter Fallujah from the Saqlawiya area," he said.

"The military operation was confronted by rebels this afternoon, and the clashes continued for three hours," he said, adding firefights were ongoing in the area.

"There are killed and wounded on both sides, and there are casualties among the civilians," he added.

Ahmed Shami, a doctor at the city's main hospital, said two people were killed and 18 others wounded in the clashes, but did not know which side the casualties were on.

Earlier, Shami said 366 people have been killed and 1,493 wounded in the Fallujah area since unrest broke out in the surrounding Anbar province in late December. He said most of the casualties were civilians who had caught in the army's shelling of the city.

Security forces have shelled Fallujah repeatedly for months.

They say they are targeting militant hideouts, but rights groups and residents say civilians bear the brunt of the bombardments.

Human Rights Watch alleged on Tuesday that the authorities have likely violated the laws of war by targeting Fallujah hospital in their conflict with militants in the city.

The crisis in the desert province of Anbar, which borders Syria, began in late December when security forces dismantled a longstanding protest camp maintained by the province's mainly Sunni Arab population to vent grievances against the government.

Militants subsequently seized parts of the provincial capital 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.

They have held all of Fallujah since, and protracted battles have continued for Ramadi.