(Adds details, fighting in Ramadi)
By Suadad al-Salhy
BAGHDAD, Jan 4 (Reuters) - Iraqi troops trying to retake Anbar province from a mixture of Islamist and tribal foes battled al Qaeda fighters in Ramadi on Saturday after shelling the western region's other main city, Falluja, overnight, tribal leaders and officials said.
At least eight people were killed and 30 were wounded in Falluja, and residents of both cities said the fighting had limited their access to food, and that they were running low on generator fuel.
Shops were sending food to mosques, and people were being asked through loudspeakers to go to collect it.
Falluja has been held since Monday by Sunni Muslim militants linked to al Qaeda and tribal fighters united in their opposition to Prime Minister Nuri al-Maliki, in a serious challenge to the authority of his Shi'ite-led government in Anbar province.
Al Qaeda's Islamic State of Iraq and the Levant (ISIL) has been steadily tightening its grip in the Sunni-dominated desert province bordering Syria in recent months in a bid to create a Sunni Muslim state straddling the frontier.
But this week's seizure of territory in Ramadi and Falluja was the first time in years that Sunni insurgents had taken effective control of the region's most important cities and held their positions for days.
In Ramadi, tribesmen and the army have been working together to counter the al Qaeda insurgents.
However, in Falluja, ISIL's task has been made easier by tribesmen who have joined its fight against the government.
Officials and witnesses said the northern and eastern parts of the city were under the control of tribesmen and militants on Saturday after residents fled to take refuge from the army shelling, and that the militants had deployed snipers atop empty houses and government buildings.
In Ramadi, military anti-terrorist teams were fighting al Qaeda militants in the streets after tribesmen asked for help from the army, which had been deployed only on the outskirts of the city, tribal sources said.
"We asked them to raid the area or bomb it with jets, but they keep refusing as they say they do not want anyone to accuse them of attacking residential areas," a tribal militia leader in Ramadi told Reuters by telephone.
Tribal leader Sheikh Rafe'a Abdulkareem Albu Fahad said the tribesmen were finding it hard to hunt down the militants in southern and eastern Ramadi as families had taken them into their homes.
"We cannot persuade the people to kick them out," he said.
The army said it controlled the entrance to Falluja and were gearing up for strikes against the militants in both cities.
"We prefer not to attack now, as the militants have been deployed among the families," said Sameer al-Shwiali, media adviser to the commander of the anti-terrorist squad.
"We call on people in Ramadi and Falluja to stay away from the militants as there will be lethal strikes targeting those militants in the coming hours."
He said at least 18 ISIL snipers had been killed since Friday night in Ramadi and Falluja.
The Iraqi Red Crescent sent convoys with food aid to both cities but could not enter because of the heavy fighting.
Tension has been running high across Anbar - the heart of Iraq's Sunni insurgency after the 2003 U.S.-led invasion - since Iraqi police broke up a Sunni protest camp on Monday. At least 13 people were killed in those clashes.
The escalating tension shows that the civil war in Syria, where mostly Sunni rebels are battling President Bashar al-Assad, who is backed by Shi'ite Iran, is spilling over to Iraq and threatening its delicate sectarian balance. (Additional reporting by Kamal Namaa; Writing by Ahmed Rasheed and Rania El Gamal; Editing by William Maclean and Kevin Liffey)