groups close in the Islamic State-held town on the road between Mosul and Raqqa, the main cities of the militant group's self-styled caliphate in Iraq and Syria.
The exodus from Tal Afar, 60 km (40 miles) west of Mosul, is causing concern among humanitarian organizations as some of the fleeing civilians are heading deeper into insurgents' territory, where aid cannot be sent to them, provincial officials said.
Popular Mobilisation units, a coalition of mostly Iranian-trained and backed militias, are trying to encircle Tal Afar, a mostly ethnic Turkmen town, as part of the offensive to capture Mosul, the last major city stronghold of Islamic State in Iraq.
About 3,000 families have left the town, with about half heading southwest, toward Syria, and half northward, into Kurdish-held territory, said Nuraldin Qablan, a Tal Afar representative in the Nineveh provincial council, now based in the Kurdish capital Erbil.
"We ask Kurdish authorities to open a safe passage for them," he told Reuters.
He said Islamic State started on Sunday night to allow people to leave after it fired mortars at Popular Mobilisation positions at the airport, south of the city, and Popular Mobilisation forces responded.
The offensive started on Oct. 17 with air and ground support from a U.S.-led coalition. It is turning into the most complex campaign in Iraq since the 2003 invasion that toppled Saddam Hussein and empowered the nation's Shi'ite majority.
The people fleeing Tal Afar are from the Sunni community, which makes up a majority in the Nineveh province in and around Mosul. The town also had a Shi'ite community, which fled in 2014 when the hardline Sunni group swept through the region.
Turkey is alarmed that regional rival Iran could extend its power through proxy groups to an area close to the Turkish and Syrian borders, where Ankara is backing rebels opposed to the Russian and Iranian-backed Syrian President Bashar al-Assad.
Citing its close ties to Tal Afar's Turkmen's population, Turkey has threatened to intervene to prevent revenge killings should Popular Mobilisation forces, known in Arabic as Hashid Shaabi, storm the town.
"People are fleeing due to the Hashid's advance, there are great fears among the civilians," said Qablan, who is also the deputy head of Nineveh's provincial council.
Iraqi Prime Minister Haider al-Abadi tried to allay fears of ethnic and sectarian killings in Tal Afar, saying any force sent to recapture it would reflect the city's diversity.
Cutting the road to Tal Afar would seal off Mosul as the city is already surrounded to the north, south and east by Iraqi government and Kurdish peshmerga forces.
Iraq's U.S.-trained Counter Terrorism Service unit breached Islamic State's defenses in east Mosul at the end of October and is fighting to expand a foothold it gained there.
AIR STRIKES ON MOSUL
Iraqi military estimates put the number of insurgents in Mosul at 5,000 to 6,000, facing a 100,000-strong coalition of Iraqi government units, peshmerga fighters and Shi'ite militias.
Mosul's capture is seen as crucial towards dismantling the caliphate, and Islamic State leader Abu Bakr al-Baghdadi, believed to have withdrawn to a remote area near the Syrian border, has told his fighters there can be no retreat.
A Mosul resident said air strikes have intensified on the western part of the city, which is divided by the Tigris river running through its center.
The strikes targeted an industrial area where Islamic State is thought to be making booby traps and transforming vehicles into car bombs, he said.
The militants are dug in among more than a million civilians as a defense tactic to hamper the strikes. They are moving around the city through tunnels, driving suicide car bombs into advancing troops and hitting them with sniper and mortar fire.
The Iraqi authorities did not release an overall estimate of the casualties, but the United Nations warned on Saturday that growing numbers of wounded civilians and military are overwhelming the capacity of the government and international aid groups.
More than 68,000 people are registered as displaced because of the fighting, moving from villages and towns around the city to government-held areas, according to U.N. estimates.
The figure does not include the thousands of people rounded up in villages around Mosul and forced to accompany Islamic State fighters to cover their retreat towards the city as human shields. It also does not included the 3,000 families which have fled Tal Afar.
In some cases, men of fighting age were separated from those groups and summarily killed, according to residents and rights groups.