The fighting prompted concern from Druze residents of the Israeli-occupied Golan Heights, and a statement from the Israeli army, which pledged to "prevent Hader from being harmed or occupied".
Almost 140,000 members of the Druze minority, which follows a secretive offshoot of Shiite Islam, live in Israel and the Israeli-occupied Golan.
The Israeli government "tactically retreated" from its decision to "support the so-called Syrian opposition from occupying the Syrian Druze village of Hader", the ministry's statement said.
Local Syrian sources described the attack as the biggest yet in the area, saying the terrorists used new routes in their assault which were reportedly opened by the Israeli army.
The Israeli Druze who broke through the fence did so in response to a major battle that was transpiring throughout Friday morning in Khader, where earlier nine people had been killed and 23 injured when a vehicle bomb exploded.
The IDF said they forced some ten villagers to return to Israel after they made it into the no-mans-land that separates Israel from Syria.
The SOHR said government troops and allied fighters were among the casualties of Friday's clashes.
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The PA ministry's statement reflects the opinion of the Syrian government, which accuses Israel of supporting terrorist groups in Syria.
The Israeli army said on Friday that it will not allow jihadists to overrun a government-held Druze village inside Syria, in an unprecedented intervention into the country's years-long civil war.
There are approximately 140,000 Druze in Israel, including 20,000 in the Golan Heights.
The move to publicly intervene in the Syrian civil war is an unusual one for Israel, which has maintained an official hands-off policy toward the conflict, only becoming involved when one of its "red lines" was violated.
After the mounting accusations, Israel showed exceptional interest in Khodr, with Prime Minister Benjamin Netanayahu telephoning Defense Minister Avigdor Lieberman to announce his support for the Druze community.
The PA ministry's statement accused Israel of supplying al-Nusra with weapons, salaries, medical aid and intelligence in exchange for keeping Israel's northern border with Syria safe. Israeli Druze attempted to help as well, as they broke through the border fence in an attempt to help their compatriots in the battle.