The UN refugee agency said as many as 70,000 Syrian Kurds had streamed into Turkey since Friday, and solidarity protests by Turkish Kurds on the border prompted clashes with security forces.
Syrian Kurdish fighters backed by reinforcements from Turkey are battling to hold off a jihadist advance on the strategic border town of Ain al-Arab, known as Kobane by the Kurds.
The IS group has seized large parts of Iraq and Syria, declaring a "caliphate", imposing its harsh interpretation of Islamic law and committing widespread atrocities including beheadings and crucifixions.
But despite US promises to expand its air campaign against IS in Iraq to Syria, there were no signs yet of American strikes in the country.
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Sahab Basravi told of his flight from Ain al-Arab.
"When the Daesh (IS) attacked Ain al-Arab, we were frightened. They said in the mosques that they could kill all Kurds between seven and 77 years old. So we collected our things and left, immediately."
He said he had not witnessed fighting or executions, but IS reputation was enough to persuade him not to stay.
IS fighters have been advancing on Ain al-Arab since late Tuesday, hoping to cement their control over a large part of Syria's border with Turkey.
Today, they were within some 10 kilometres (six miles) of the town, after capturing more than 60 villages in the area, the Syrian Observatory for Human Rights said.
The fighting has killed at least 27 Kurdish militants and 39 IS jihadists, according to the Britain-based monitoring group.
At the border today, Turkish security forces used tear gas and water cannon to disperse a solidarity protest by Turkish Kurds and later closed most border crossing points in the area, including one used by Kurdish fighters heading to Syria.