ANKARA, Turkey — Fighters from the Islamic State have been storming through Kurdish villages in northern Syria in recent days, clashing with Kurdish militias, terrifying residents and sending tens of thousands of new refugees fleeing across the border into Turkey.

A United Nations official said Sunday that the refugee crisis near the Syrian border town of Ayn al-Arab, known as Kobani in Kurdish, could be one of the greatest refugee flows since the civil war in Syria began.

“I don’t think in the last three and a half years we have seen 100,000 cross in two days,” said Carol Batchelor, the Turkey representative for the United Nations’ refugee agency, according to Reuters. “So this is a bit of a measure of how this situation is unfolding and the very deep fear people have about the circumstances inside Syria and, for that matter, Iraq."

Ms. Batchelor said that if the crisis continued, the number could rise into the hundreds of thousands.