"It is a critical moment to protect children and open safe routes to allow the 1.5 million civilians, including about 600,000 children, still trapped in the city to leave safely," the charity said.
Iraqi forces reached the edges of Mosul on Tuesday, two weeks into a massive operation to retake the city they lost to the Islamic State jihadist group in June 2014.
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"We cannot sit back and wait for another situation like Aleppo to unfold, whilst there is still the opportunity to get children out of the war zone," the NGO's Iraq director Maurizio Crivellaro said.
An estimated 250,000 people have been besieged by regime forces in the northern Syrian city of Aleppo for three months.
Most estimates put the number of people trapped in Mosul at more than a million, but accurate numbers are impossible to come by after more than two years of jihadist rule in the city.