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Hundreds of thousands of civilians remain in Mosul, which was seized by the Islamic State group in 2014, and officials and witnesses have said that air strikes have taken a devastating toll on civilians in the city this month.
"Just arrived in Iraq to focus on the dire humanitarian situation on the ground. Protection of civilians must be the absolute priority," a post on the UN chief's official Twitter account said.
Guterres was to meet top Iraqi officials including Prime Minister Haider al-Abadi in Baghdad before flying to Arbil, the capital of the country's autonomous Kurdish region.
In addition to civilians caught in the crossfire inside the city, many more have fled their homes to escape the fighting.
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According to Iraqi authorities, more than 200,000 civilians have fled west Mosul since the operation to retake it was launched last month.
IS overran large areas north and west of Baghdad in 2014, but Iraqi forces backed by US-led air strikes have since regained much of the territory they lost.
Iraqi forces launched a major operation to retake Mosul in October, retaking its eastern side before setting their sites on the smaller but more densely populated west.