"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agreements] stipulate that this de-escalation zone should consolidate stability, while all non-Syrian forces must be withdrawn from this area", Lavrov said.
"Since the beginning of the crisis, Iran has supported Syria in the war against terrorism backed and financed regionally and internationally", he said.
Israeli officials have maintained that they can not tolerate a continued Iranian military presence in Syria.
The Defense Department's warnings for Syria come amid reports that Iranian and Iranian-backed Hezbollah fighters may have begun withdrawing from areas in southern part of the country close to the tense border with Israel.
Mr McKenzie said the USA troops and their local militia allies were staying in At-Tanf, dismissing Assad's call for their withdrawal.
The Syrian president said his government had "opened doors to negotiation" with US-backed Syrian Democratic Forces (SDF), a predominantly Kurdish group that controls parts of northern Syria. Subsequently, Iranian officials including Shamkhani and IRGC PR Chief Ramezan Sharif threatened Israel with "retaliation at the right time". To start, being forced to withdraw from Syria would be a major blow to Iran's prestige at a moment when its economy is bracing for crippling sanctions following America's withdrawal from the 2015 nuclear deal.
It's too soon to say whether Israel's diplomacy with Russian Federation will result in the removal of Iran and its allied militias from Syria altogether.
The minister's statements came after similar ideas were expressed by the Syrian President Bashar Assad in his interview with RT.
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Israel has claimed to have hit Iranian military targets in Syria in recent weeks and Prime Minister Benjamin Netanyahu has said Tel Aviv would not allow Iran to establish any military bases in Syria.
A day earlier, Russian Ambassador to the UN Vasily Nebenzya said he believed an agreement has been reached on the withdrawal of Iranian forces from the border between Syria and the Israeli-occupied Golan Heights.
Syria's foreign minister says Iranian military advisers are embedded with Syrian troops but Tehran has no combat forces or fixed bases in the country.
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.
Shamkhani said Iran strongly supports Russia's efforts to purge the Syrian-Jordanian border of terrorists and restore the Syrian army's control over the region.
"Neither Turkey, nor U.S. has a right to negotiate [about] the [fate of the] Syrian cities", he said, as cited by the Syrian SANA state news agency.
"We have Iranian officers who work with the Syrian army as help, but they do not have troops", he said.