Rebels hold stretches of that area and intensive Israeli airstrikes in Syria this month were prompted by what Israel said was Iranian rocket fire from the area into the Golan Heights. Moscow has also agreed not to try to stop Israeli bombing raids on Iranian bases and militias elsewhere in the country.
Meanwhile, Israel is meeting with USA officials to hammer out the details of a joint strategy for dealing with Iran's presence in the Middle East.
The Israeli prime minister is scheduled to meet with European leaders next week and said that he intends to discuss Iran's nuclear power and find ways to block its "nuclear aspirations" and "Iran's spreading in the Middle East".
Government forces recently dropped leaflets on rebel-held areas in Daraa, warning of an imminent offensive and urging anti-Assad fighters to lay down their arms.
The territory is covered by a ceasefire agreement signed a year ago between the US, Russia and neighbouring Jordan.
According to the report, the understandings were reached in a series of indirect meetings in Jordan, where Iranian officials, including the envoy to Jordan, met with top Jordanian officials, who in turn met with senior Israeli security officials..
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Jordanian officials served as mediator, shuttling messages between the two rooms, according to the report.
Israel is vehemently opposed to Iran maintaining a military presence in Syria, however.
Russian Federation and Iran are close allies of Syrian President Bashar al-Assad.
One participant told Elaph that the Iranians "arrived at a quick agreement" that its forces would not intervene in fighting near the Golan Heights and the Israel-Jordan border, surprising the Israeli representatives.
The source added that the Syrian government will order the Syrian Army and the wider coalition of government forces to liberate the entirety of Syria.