Damascus has not engaged in talks about the south, and any agreement over that region must include the pullout of USA forces, he said.
Syrian forces, backed by Russian air power and Iranian-backed militias, will "liberate by force" rebel- and Islamic State-held territory, Mr. Assad said.
"We will continue to act against [Tehran's] intention to establish a military presence in Syria across from us, not just across from the Golan Heights but anywhere in Syria", he said.
On May 31, Israeli ambassador in Moscow Gary Koren told TASS the Israeli government was satisfied with Russia's position on the Iranian military presence on the Syrian-Israeli border.
Mr McKenzie said the United States troops and their local militia allies were staying in At-Tanf, dismissing Assad's call for their withdrawal.
In this photo released by the Syrian official news agency SANA, Syrian Foreign Minister Walid al-Moallem speaks during a press conference in Damascus, Syria, Saturday, June 2, 2018.
"Since the beginning of the crisis, Iran has supported Syria in the war against terrorism backed and financed regionally and internationally..." Subsequently, Iranian officials including Shamkhani and IRGC PR Chief Ramezan Sharif threatened Israel with "retaliation at the right time".
Tensions between Washington and Damascus boiled over in April, when USA and allied warplanes launched a series of airstrikes against suspected chemical weapons facilities in Syria.
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.
Israel must demand a full accounting of the Iranian forces in Syria and that any agreements made on the south be based on verification.
In the meantime, the Russian Hmeimim air-base announced Thursday that forces of the Fourth Syrian Army division are heading towards southern Syria in order to fight the Jubhat al-Nusra militias.
Many dead, including women and children, in mindless CHEMICAL attack in Syria. In the previous year, Netanyahu and his top ministers have stepped up diplomacy with Moscow to make the strategic case that it's not in Russia's interest to allow Iran to turn Syria into a client state like Lebanon, according to USA and Israeli officials.
Rebels control stretches of southwest Syria, bordering the Israeli-occupied Golan Heights, while Syrian army troops and allied Iran-backed militias hold nearby territory.
Backed by Russian air power and Iranian and Hizbullah militias on the ground, Assad's forces have gained significant ground in recent months in the seven-year civil war that has killed an estimated half a million people and driven another 5 million overseas as refugees.
Ahead of Lieberman's visit Russian Foreign Minister Sergei Lavrov said all non-Syrian forces should withdraw from the southern border area of Syria.
Mr Assad said Iran's presence in Syria was limited to officers assisting the army.