ANKARA, Turkey — The number of Syrian refugees who have reached Turkey in the past four days after fleeing the advance of Islamic State militants now totals 130,000, Turkey’s deputy prime minister said Monday.

Numan Kurtulmus warned that the number could rise further but insisted that Turkey was ready to react to “the worst case scenario.”

“I hope that we are not faced with a more populous refugee wave, but if we are, we have taken our precautions,” Kurtulmus said. “A refugee wave that can be expressed by hundreds of thousands is a possibility.”

The refugees have been flooding into Turkey since Thursday, escaping an Islamic State offensive that has pushed the conflict nearly within eyeshot of the Turkish border. The conflict in Syria has pushed more than a million people over the border in the past 3½ years.

The al-Qaida breakaway group, which has established an Islamic state, or caliphate, ruled by its harsh version of Islamic law in territory it captured straddling the Syria-Iraq border, has in recent days advanced into Kurdish regions of Syria that border Turkey, where fleeing refugees on Sunday reported atrocities that included stonings, beheadings and the torching of homes.