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, also known as Kobani.
A Kurdish commander on the ground said the ISIL had advanced to within 15 km (9 miles) of the town.
Local Kurds said they feared a massacre in Kobani, whose strategic location has been blocking SIL militants from consolidating their gains across northern Syria.
The United States has said it is prepared to carry out airstrikes in Syria to stop the advances of the ISIL, which has also seized tracts of territory in neighboring Iraq and has proclaimed a caliphate in the heart of the Middle East, Reuters reported.
US forces have bombed the group in Iraq at the request of the government, but it is unclear when or where any military action might take place in Syria.
Lokman Isa, a 34-year-old farmer, said he had fled with his family and about 30 other families after the heavily armed ISIL militants entered his village of Celebi. He said the Kurdish forces battling them had only light weapons.
"They (ISIL) have destroyed every place they have gone to. We saw what they did in Iraq -- in Sinjar -- and we fled in fear," he told Reuters in the Turkish town of Suruc, where Turkish authorities were setting up a camp.