Meanwhile, Turkey's PKK Kurdish rebel group on Monday called on fellow Kurds to cross into Syria and combat ISIL insurgents besieging a town near the border, the pro-Kurdish agency Firat reported.
"The number of Syrians has passed 130,000," Kurtulmus told reporters in Ankara, warning that the number would likely rise.
ISIL extremists 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.
"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 Monday by Turkey's emergencies directorate.
"Some of the incoming refugees are due to stay at their relatives' houses in Turkey, and some will be transferred to the camps," a Turkish official told AFP.
The UN refugee agency, the UNHCR, on Saturday said that as many as hundreds of thousands of refugees might flee.