The Israeli military, contacted by AFP, said it could not comment.
Mohamed Mreiwel, mayor of the village of Jabata al-Khashab in Quneitra province, said on Monday that he had met three times with Israeli officials who had asked to see him.
Israel, long a foe of Syria, has launched hundreds of strikes on Syrian military sites since the fall of president Bashar al-Assad on December 8, destroying most of the army's arsenal, a war monitor has said.
The same day Assad was toppled by Islamist-led forces, Israel also announced that its troops were crossing the armistice line and occupying the UN-patrolled buffer zone that has separated Israeli and Syrian forces on the strategic Golan Heights since 1974.
Mreiwel said that in his first meeting with the Israelis, "they asked for weapons to be handed over to them within 48 hours".
Residents of the village, which is located in the buffer zone, had complied with the request, he said.
Syria's army collapsed in the face of the rebel offensive, with thousands of soldiers, policemen and other security officials deserting their posts.
Some Syrians seized weapons left behind by soldiers and security personnel, Mreiwel said, with the Israeli army "dedicating an area for people to hand over those weapons".
During his latest meeting with the Israelis on Sunday, "we told them that we no longer had any weapons and that if we had any, we would hand them over to the Syrian government", said Mreiwel.
He added that he told the Israeli officials that "we are not allowed to meet with you", as Syria and Israel are still technically at war and do not have diplomatic ties.
Israeli troops have conducted patrols on the main street of Jabata al-Khashab, an AFP correspondent said.
Israeli tanks are also stationed in nearby Baath City, named for the now suspended political party that ran Syria for decades until Assad's ousting.
Israel seized much of the Golan Heights from Syria in war in 1967, later annexing the territory in a move largely unrecognised by the international community.
