Syrian Kurdish fighters say they have stopped the advance of the Islamic State in Iraq and the Levant (ISIL) group in northern Syria near the Turkish border.

The Kurdish forces engaged in heavy clashes with ISIL fighters on Monday, as the group laid siege on an area east of the city of Kobane in Aleppo province, a spokesman said.

More than 130,000 Syrian Kurds have fled across the border into Turkey, escaping the advance by ISIL, Turkish Deputy Prime Minister Numan Kurtulmus said, warning that the number would probably rise.

ISIL have seized dozens of villages in the past week as they advance on the town of Ain al-Arab, called Kobane in Kurdish, near the border.

The Syrian Observatory for Human Rights, which tracks violence in the Syrian war, said ISIL fighters had made no significant advance in the last 24 hours.

"If ISIL attacks continue in the Kobane region, Turkey may face an intensive influx," Kurtulmus said.

"We have taken all necessary measures in case of a continued influx of displaced people. We don't want that, of course, but we are ready," he added.

The latest total was a sharp increase from a figure of 104,000 given earlier on Monday by Turkey's emergencies directorate.

The UN refugee agency, the UNHCR, on Saturday said that as many as hundreds of thousands of refugees might flee.

"We are ready for the worst scenario," Kurtulmus said. "The number of displaced people has not reached that level, but we will do everything to welcome those entering Turkey."

Until the ISIL assault, Kobane, the third biggest Kurdish population centre in Syria, had been relatively safe, sheltering 200,000 people displaced from elsewhere in Syria.

Turkey's emergencies directorate, the AFAD, said authorities were clamping down at the border with Syria.

"The border is open, but only at one place at Mursitpinar, for better organisation of crossings," an AFAD official said.

"A single point has been opened for displaced Syrians, so that we can do identity control and give first aid, vaccinating people if necessary," the official said.