This family is among those fleeing Fallujah
Thousands of residents are fleeing the Iraqi city of Fallujah, amid artillery fire and air strikes by government forces, witnesses told the BBC.
The exodus comes after the government admitted it had lost control of the city - west of Baghdad - to al-Qaeda-linked militants and allied tribesmen.
Fighting is also reported in Ramadi, also in Anbar province, parts of which are in the hands of militants.
Both the US and Iran have offered military support, though not troops.
Fallujah is a highly symbolic city for many Iraqis, particularly Sunni Arabs, say correspondents.
It is remembered for the battles fought there between insurgents and US-backed forces in 2004.
The latest upsurge in violence in Anbar began after troops broke up a protest camp by Sunni Arabs in the city of Ramadi on Monday.
Separately on Sunday, bombs in the capital Baghdad left at least 19 people dead. The deadliest attack, which police and medical sources told Reuters had killed nine and wounded 25, was in the Shia district of Shaab.
Local journalist and Fallujah resident Ahmad al-Jumaili told the BBC that the city had been targeted by artillery fire and air strikes since Monday, and that a heavy bombardment continued on Sunday.
Some specific districts were under attack, he said - al-Askari (in the east), al-Shuhada (in the west), al-Nazzal and al-Andalus (central), and al-Jughifi (in the north).
Fallujah is highly symbolic for Sunni Arabs, who call it the
"Jerusalem" of Iraq and the "city of mosques and
minarets". For them, the city is an emblem of resistance
against, in their words, the "occupiers" and "oppressors"
over the years.
Sunni Arabs further remember Fallujah for the battles
fought by tribesmen and insurgents against US-backed
Iraqi troops in 2004, and finally for sparking off the anti
government protests in late 2012 against what Sunni
Arabs called marginalisation of their community.
But it was the government's decision on 30 December to
break up a protest camp in Ramadi, another city in Anbar
province, and the subsequent arrest of a Sunni MP that
provoked Fallujah residents and al-Qaeda militants to join
forces against the regular security forces.
"The army is using a military camp known as Tarik on the eastern outskirts of Fallujah as a launch pad for its strikes," Mr Jumaili said.
"Thousands of families have fled their homes to near villages fearing for their lives and as the city is hit by severe shortage of food and fuel supplies."
Other residents confirmed the exodus. It came as a senior regional Iraqi army commander, Lt Gen Rasheed Fleih, said it would take "two to three days" to eject the militants from Fallujah and Ramadi.
Al-Qaeda-linked militants the Islamic State in Iraq and the Levant, known as ISIS, are reported to control the south of Fallujah.
Tribesmen allied with al-Qaeda hold the rest of the city.
Reports also speak of air strikes and clashes in Ramadi.
Iran's deputy chief of staff Gen Mohammad Hejazi offered military equipment and advice to Iraq to help it battle al-Qaeda, reported the official Irna news agency.
It followed comments from the US Secretary of State John Kerry, who said the US would help Iraq fight al-Qaeda-linked militants, but that it was not planning to send troops back to the country.
The fighting in Anbar comes against the backdrop of swelling anger among Sunni Arabs at what they say is their marginalisation by the Shia-led government.
They say their minority community is being targeted by anti-terrorism measures implemented to stem the surge in sectarian violence.
For many Fallujah residents, the Iraqi army is serving the "sectarian" agenda of Prime Minister Maliki's Shia-led government, says BBC Arabic analyst Ahmed Maher.
But among other Iraqis, Fallujah is also known as the "city of terrorism" as it served as the nucleus of al-Qaeda in their country. After the US-led invasion in 2003, al-Qaeda based itself in Fallujah where several beheadings and killings of foreigners took place.
In recent months, Sunni militants have stepped up attacks across Iraq, while Shia groups began deadly reprisals - raising fears of a return to full-scale sectarian conflict.
On Wednesday, the United Nations said at least 7,818 civilians and 1,050 members of the security forces had been killed in 2013.
The annual death toll was the highest in years, but still significantly below those recorded at the height of the insurgency in 2006 and 2007.
US forces ended combat missions in Iraq in 2010 and left the country in late 2011, having entered in 2003 in a US-led invasion to remove Saddam Hussein from power.