The recapture of Dara'a is highly important because it borders the occupied Golan Heights which Israel has used to treat wounded militants for years.
"Israel appreciates Russia's understanding of our security needs, especially with regard to the situation on our northern border", Lieberman said following his meeting.
Scores of Iranian soldiers have been killed in battles with insurgents in Syria, including a number of officers.
In an interview with the Shargh daily published on Saturday, he said that Iran's defense strategy has been drawn up based on the experiences of the 1980-1988 Iran-Iraq war and proportionate to threats.
But it appears only a matter of time before Damascus moves its forces south. Russian Federation has hinted that "foreign forces" should withdraw from Syria, and Israel has interpreted that to include Iran.
SDF continue to fight against ISIS in part of oil-rich province of Deir Al Zour.
Israel has enjoyed amicable relations with Moscow regarding Syria since 2015, when Russian Federation began to intervene more heavily in the Syrian conflict. However, neither Jerusalem, nor Moscow, publicly acknowledged any agreement between the sides regarding Iran's military presence in Syria.
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"Contrary to the unlawful presence of the U.S. and some regional countries in Syria, Iran's presence is not imposed and is not the result of an illegal military aggression", he told the Shargh newspaper, according to state-run Press TV. This comes as Russia's United Nations envoy tells reporters about Moscow's agreement with Tel Aviv on the withdrawal of Iranian forces from southern Syria.
"We are the most careful to return the displaced people to their homes and we will provide all facilitations to those who want to return", al-Moallem added. "They [the agreements] stipulate that this de-escalation zone should consolidate stability, while all non-Syrian forces must be withdrawn from this area", Lavrov said. The U.S. has military advisers based in Tanf.
"The U.S. presence in Syria is illegitimate and they should withdraw from al-Tanf and any other area in Syria", he noted.
Russian Federation said last week that only Syrian army troops should be on the country's southern border with Jordan and Israel. The cease-fire means the Syrian rebels have continued to control an area along the Golan and Jordan's border.
The Arab newspaper also reported that Jerusalem political sources said that Israel and Russian Federation have reached an understanding that would let the Assad forces to take back control over the southern part of the country, near the border area, in exchange for an evacuation of the Iranian forces.
The problem with discussions about Iran's involvement in Syria and promises that it should withdraw or reduce its presence, is that the Syrian regime denies Iran is even present in Syria in any significant way.