The areas are now held by the units of the so-called Free Syrian Army backed by the US.
There has been a hike in Israeli strikes since the collapse late previous year of the Daesh Takfiri terrorist group, something that significantly demoralized other militant groups operating against Damascus.
"Don't believe anything that is said about an agreement on the south until you see that the United States has withdrawn its forces from the At-Tanaf base", he said. He also reiterated that the presence of the United States forces on the Syrian territory is illegal.
Israel has for long demanded the pullout of Iranian forces from Syria's southern borders, and launched multiple airstrikes on Syrian military positions on the pretext that Iranian fighters are running them.
The attack triggered US, French and British missile strikes against what they called chemical weapons targets, the first coordinated Western strikes against Mr Assad's government of the war.
Al-Muallem added at a press conference, "we sent 50 names, the Syrian state should have the majority in any number which will be agreed upon, and the committee's decisions should be taken unanimously". "If not, we're going to resort.to liberating those areas by force".
His remarks came after Assad told Russian broadcaster RT he would not hesitate to use force to retake the third of the country held by the Syrian Democratic Forces.
Assad added that "the Americans should leave".
"We have one option: to live with each other as Syrians".
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Over the years, Israel has watched as different groups in southern Syria came to control different parts of the area near the Golan border.
In the meantime, U.S. activities at the At-Tanf base are becoming increasingly questionable.
There has been no confirmation of a deal between Russia, Israel and Iran however.
The situation in southern Syria is increasingly drawing the attention of all parties involved in the Syrian conflict.
"It must withdraw its forces from At-Tanaf".
"Since the beginning of the crisis, Iran has supported Syria in the war against terrorism backed and financed regionally and internationally...[there is] no Iranian military presence [in] the Syrian territories; rather, there are advisers who work by the side of the Syrian Arab Army", Syria's official SANA news agency reported Walim Moallem saying.
Shamkhani further rejected media reports that Iranian officials have held a meeting with Israeli intelligence agents in the Jordanian capital Amman, describing it as a "baseless" rumour aimed at legitimatizing the Israeli regime and weakening the will of resistance movements fighting the regime.
Ali Shamkhani, secretary of Iran's Supreme National Security Council, said Iranian troops are only serving in Syria in an advisory capacity and that Iran has no military base there.