* Locals accuse Baghdad of indiscriminate bombardment
* City west of capital held by Islamic State since January
* Iraq fractures along sectarian and ethnic lines
* 10 killed in suicide car bomb attack in Baghdad (Adds suicide car bomber attack in Baghdad killing 10)
By Kamal Namaa
FALLUJA, Iraq, July 22 (Reuters) - Iraqi government air strikes killed 19 people, including children, in Falluja on Monday and Tuesday, a health official in the militant-held city said.
The Iraqi army has been shelling Falluja, 70 km (44 miles) west of Baghdad, for months, trying to drive out the Sunni militants from the group now known as Islamic State. The insurgents, backed by discontented local Sunni tribal leaders, overran the city in January.
Ahmed al-Shami, a spokesman for the Falluja health office - the local arm of the health ministry - said the 19 dead included women and children and that Falluja hospital had also received 38 wounded people since Monday evening.
Residents of Falluja and the nearby town of Garma said helicopters fired artillery and dropped three barrel bombs on Falluja and two on Garma.
Barrel bombs - powerful makeshift weapons made from high explosives, cement and metal parts packed into oil drums, usually dropped from helicopters - have gained notoriety in the region because of their use in neighbouring Syria by President Bashar al-Assad's forces to flatten buildings in rebel-held areas.
Scores of people have died since January in what residents describe as indiscriminate bombardment. In May, witnesses in Falluja said barrel bombs had been dropped on the city.
The government denies indiscriminate attacks, saying it targets insurgents, but a mid-level security officer in Anbar province has previously confirmed that barrel bombs have been dropped on Falluja.
Prime Minister Nuri al-Maliki's military spokesman, Lieutenant General Qassim Atta, was not immediately available to comment on this week's attacks.
Some 560,000 people have fled Anbar province - the large area of western Iraq where Falluja is situated - since the Islamic State takeover in January, according to the International Rescue Committee, a New York-based humanitarian organisation.
Islamic State took over a swathe of northern territory last month in an assault that caused large numbers of government soldiers to desert, shifting the main battleground in a civil war that pits the Shi'ite-led Baghdad government against a well-equipped Sunni insurgency.
Maliki's office said on Tuesday he had met Sunni tribal leaders from several provinces where the conflict is raging. Anger with Maliki's government has encouraged some Sunni armed groups to stick with the hardline Islamic State despite ideological differences, officials and tribal leaders say.
The conflict, which threatens to break up Iraq along ethnic and sectarian lines, has killed almost 5,600 civilians this year, according to the latest United Nations figures.
Ten people, six of them policemen, were killed late on Monday when a suicide bomber drove a car into a checkpoint at the entrance to the mostly Shi'ite Kadhimiya district of northern Baghdad.
In the mainly Shi'ite town of Nahrawan east of Baghdad, a car bomb exploded in a market on Tuesday, killing five people and wounding 13, police and medical sources said.
A roadside bomb targeting an army patrol in the Abu Ghraib area west of Baghdad killed one soldier and wounded four, police and medical sources said. Two mortar rounds landed in the mostly Shi'ite area of Sabaa al-Bour just north of the capital, killing one person, police and medics there said.
The Islamic State has claimed responsibility for several recent bombings in the capital, including the wave of car-bomb attacks on Saturday that killed at least 27 people.
In the town of Abu al-Khaseeb, south of the predominantly Shi'ite city of Basra, gunmen broke into a Sunni mosque on Tuesday during prayers, killing the preacher and kidnapping four men who were praying, police sources said.
The body of one of the kidnapped men was found dumped on the side of a road near the mosque, the sources said. (Additional reporting by Ahmed Rasheed in Baghdad; Writing by Maggie Fick; Editing by Robin Pomeroy/Ruth Pitchford/Larry Kign)