Tens of thousands of Syrian Kurds have crossed into Turkey over the past two days, fleeing an advance by fighters from the Islamic State of Iraq and Levant (ISIL), who have seized dozens of villages close to the border, the UN's refugee agency says.

By Sunday, more than 70,000 refugees had crossed the border, said the UNHCR.

Meanwhile, Kurdish forces in Turkey issued a new call to arms to defend a border town in northern Syria from advancing ISIL fighters. 

Turkey opened a stretch of the frontier on Friday after Kurdish civilians fled their homes, fearing an imminent attack on the border town of Ayn al-Arab, known as Kobani in Kurdish.

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"There was bombing all around us. We were in the city and ISIL attacked us, and we ran away. We all left there in a hurry," said Feride Ibrahim, a Syrian refugee.

The refugees, who fled fighting between ISIL and Kurdish fighters, had been amassing along the border since Thursday.

ISIL's advances in northern Syria have prompted calls for help by the region's Kurds who fear an impending massacre in Kobani, which sits in a strategic position close to the Turkish border.

A Kurdish politician from Turkey who visited Kobani on Saturday said locals had told him that ISIL fighters were beheading people as they went from village to village.

"Rather than a war this is a genocide operation ... They are going into the villages and cutting the heads of one or two
people and showing them to the villagers," Ibrahim Binici, a deputy for Turkey's pro-Kurdish HDP, told Reuters.

"It is truly a shameful situation for humanity," he said, calling for international intervention.

Iraqi Kurdish leader Masoud Barzani on Friday made a similar appeal to protect Kobani from the ISIL advance, saying the fighters must be "hit and destroyed wherever they are".

The US is drawing up plans for military action in Syria against ISIL, which has seized larges expanses of territory in Syria and Iraq, proclaiming a caliphate in the heart of the Middle East.

Addressing a session of the UN Security Council on Iraq on Friday, US Secretary of State John Kerry said that Iran could play a key role in confronting and eliminating ISIL in Iraq.

Kerry said there was a role for nearly every country in the world to defeat what he described as a "militant cult masquerading as a religious movement".