Lavrov's comment apparently referred to areas including the Syrian Golan Heights region abutting the Israeli Golan Heights and the border with Jordan, and indicated that Russian Federation was open to Israeli demands that Iranian forces be kept far from Israel's borders.
The top Syrian diplomat further rejected Israeli claims that Iran had military bases in the Arab country, saying that the Tel Aviv regime made such propaganda in an effort to try and pressure Iran.
Iran has pledged that it would punish Israel for the deadly air raid.
Mr Assad said Iran's presence in Syria was limited to officers assisting the army.
Since Iran and Russian Federation reached an agreement in the summer of 2015 to coordinate a military campaign to save the regime of Syria's dictator, that war has held together an unholy alliance of those three states.
Iran has repeatedly said in the past that it only has advisers in Syria but thousands of Iran-backed groups from Lebanon, Iraq, Pakistan and Afghanistan have played instrumental role in helping government forces regain control of areas held by insurgents.
SDF continue to fight against ISIS in part of oil-rich province of Deir Al Zour.
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Iranian forces and those of its proxy, Hezbollah, are preparing to leave southern Syria, the Syrian Observatory for Human Rights reported.
Located on Syria's border with Jordan, Al-Tanf was captured past year by the USA, which declared it under its protection and attacked pro-government forces showing up there.
"Any interested party in Syria should understand that attacking US Forces or our coalition partners will be a bad policy", Lieutenant General Kenneth McKenzie, director of the joint staff, said during a press conference. "There are no fixed military bases for the Islamic Republic of Iran and what Israel is circulating are lies".
"As long as there is war on terrorism, Syria as a sovereign state will co-operate with whoever it wants in fighting terrorism", he said.
"It is necessary to discuss everything about the situation on the border, in the southern de-escalation zone, where we have an agreement with Jordan and the US", Shoigu reportedly told Lieberman.
On Saturday, Channel 10 reported that Israeli officials had denied claims by Russia's ambassador to the United Nations that it has reached an agreement with Moscow on the withdrawal of Iranian forces from southwest Syria.
Months after an alleged chemical attack by government forces prompted US President Donald Trump to call the Syrian president "Animal Assad" in a tweet, Assad said he had no nickname for Trump.
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Al-Moallem said that only when US troops withdraw from the Tanf area near the Jordanian border can an agreement be discussed.
US forces are based in a southern desert pocket further east at Tanf, a strategic highway border crossing with Iraq.
"The U.S. troops should withdraw from Syria and Syrian sovereignty over the Tanf area is undoubted", he said.
The Syrian government hopes to restore military presence in Daraa and Qunaitera after the evacuation of rebels, in order to control all border points between Daraa and Jordan as well as areas between Quanitera and the Israeli-occupied Golan Heights, while activating the 1974 Disengagement of Forces Agreement between Syria and Israel.
Russian Federation gave Israel a "green light" to attack Iranian bases inside Syria during conversations between senior leaders over the last two days, according to a Saudi newspaper report published Friday.
"It also has another message that the era of "hit-and-run" has ended and the regime should be responsible for its behavior", the Iranian official pointed out.
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