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SOUTH OF MOSUL, Iraq (Reuters) - A few hundred civilians have fled their homes in the outskirts of western Mosul, the first reported displacement since a U.S.-backed offensive on the jihadists’ remaining stronghold there began at the weekend.

A Reuters correspondent saw about 200 women and children being transported on buses by federal police on Wednesday to the town of Hammam al-Alil, some 20 km (12 miles) south of Mosul, where camps have been set up.

They said they had fled heavy bombardment in two villages near Mosul’s airport, which is now in the crosshairs of Iraqi forces and could become a close support base for the push deeper into the city.

The federal police and elite Interior Ministry units known as Rapid Response have made quick progress towards western Mosul in a sweep from the south through hilly desert terrain since fighting resumed on Sunday.

They have been advancing so far in sparsely populated areas, but the fighting is expected to get tougher as they enter the city itself and the risk to roughly 750,000 civilians there will rise.

Up to 400,000 people could be displaced from western Mosul where residents are already suffering food and fuel shortages and many markets have closed, according to the United Nations.

Western Mosul contains the old city center, with its ancient souks, government administration buildings and the mosque from which Islamic State leader Abu Bakr al-Baghdadi proclaimed his self-styled caliphate over parts of Syria and Iraq after rapid advances in 2014.

Islamic State is essentially under siege in western Mosul after being driven out of districts east of the Tigris river in 100 days of heavy fighting that ended a month ago.

About 160,000 civilians have been displaced from the Mosul area since the start of the battle in October, U.N. officials say. Many more people have remained in their homes despite the violence.