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The United Nations says about 100,000 people have fled into Ethiopia from the self-declared republic of Somaliland in the past month.
Many others are internally displaced following fighting in the disputed city of Las Anod which has killed more than 200 people.
The UN said the refugees have gathered in the Doolo region of Ethiopia which is enduring its worst drought in four decades.
It takes aid workers two days of driving to reach the refugees who are sheltering in public buildings or sleeping outside.