A Syrian government offensive in the southwest has uprooted more than 120,000 civilians, driving most of them towards the border with Jordan and the Israeli-occupied Golan Heights, a war monitoring group said on Friday.
A senior Israeli minister said refugees gathering at the Golan frontier must be prevented from crossing into Israel.
Jordan, already hosting some 650,000 Syrian refugees, also says its border will remain closed to more refugees.
Syrian government forces backed by Russian air power have turned their focus to the rebel-held southwest since defeating the last remaining insurgent pockets near the cities of Damascus and Homs.
Their advances in areas east and northeast of Daraa city, and bombardment of the heavily populated rebel-held town of Nawa to its northwest, have triggered a mass flight of civilians.
The Syrian Observatory for Human Rights said tens of thousands had gathered at Syria's border with Jordan while thousands more had fled to the Golan frontier, many of them from Nawa.
Observatory Director Rami Abdulrahman, speaking by phone, said some people had also crossed into government-held areas, while others had gone to a corner of the southwest held by an Islamic State affiliated group.
“I think we must prevent the entry of refugees from Syria to Israel, in the past we have prevented such cases,” Israeli Energy Minister Yuval Steinitz, a senior minister, told a Tel Aviv Radio.
Jordan says the international community must find ways to support Syrians inside Syria. “Jordan has reached its capacity in receiving refugees,” Foreign Minister Ayman Safadi told the pan-Arab broadcaster al-Jazeera late on Thursday, affirming the government position.
The Syrian war has already displaced 6 mln people inside Syria and driven 5.5 mln abroad as refugees.