Moscow has also agreed not to try to stop Israeli bombing raids on Iranian bases and militias elsewhere in the country.
It is understood that, for its part, Israel agreed to accept the return to the border of soldiers loyal to Assad'd regime; while Russian Federation will guarantee that no Iranian or Hezbollah forces return to the area.
The Israeli and Russian defence ministers, Avigdor Lieberman and Sergei Shoigu, are due to meet on Thursday.
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After liberating the entirety of Damascus city and the broader province from an array of hardline Islamist militant groups, including the Daesh* terrorist group, the Syrian Army and other government forces are set to launch a major offensive in southern Syria, near the Arab Republic's border with Israel.
Israel has warned Iran of the possibility of conflict should Tehran send its troops and Hezbollah terrorists to southern Syria in order to participate in the fighting there.
"When you consider the advanced weapon systems - surface to surface missiles and anti aircraft systems - that the Iranians want to deploy in Syria, it becomes clear that they must be prevented from doing so in all of Syria and not only within a limited distance from the Israeli border", Chagai Tzuriel, director-general of the intelligence ministry, told Reuters.
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Prime Minister Benjamin Netanyahu also said in remarks to the Knesset on Monday that Iran should be pressured to leave Syria altogether. "The Iranians provided assurances that their forces would not operate alongside the Syrian military in the offensive", a senior Jordanian official who took part in the mediation efforts told the Saudi website.
Moscow, Syrian President Bashar al-Assad's ally, brokered a string of de-escalation zones for insurgent enclaves past year, though fighting raged on in some. One participant in the talks reportedly said that "the sides discussed this issue with the Israelis, and arrived at a quick agreement that even surprised the Israeli representatives".
Those strikes followed a barrage of some 32 rockets that were fired by Iranian forces in Syria towards Israel's part of the Golan Heights.
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An aviation red alert was in effect due to risks ash could be carried into aircraft routes and damage jet engines, USGS said. The USGS said, Depending on weather conditions, that the ash might fall as far as Hilo, 30 miles to the northeast.