Russian Foreign Minister Sergei Lavrov said on Monday that only Syrian government troops should have a presence on Syria's southern border, which is close to Jordan and Israel.
Rebels hold stretches of that area and intensive Israeli air strikes in Syria this month were prompted by what Israel said was Iranian rocket fire from the area into the Golan Heights.
Russia and Iran are close allies of Syrian President Bashar Al Assad.
"Of course, the withdrawal of all non-Syrian forces must be carried out on a mutual basis, this should be a two-way street," Mr Lavrov said at a joint news conference in Moscow with Jose Condungua Pacheco, his counterpart from Mozambique.
"The result of this work which should continue and is continuing should be a situation when representatives of the Syrian Arab Republic's army stand at Syria's border with Israel," Mr Lavrov said.
The Syrian Observatory for Human Rights has reported Syrian army movements into the south and state media have reported leaflet drops on rebel-held areas there urging insurgents to accept government rule, two signs a military offensive may be coming.
Israel called on Monday for its arch-foe Iran to be denied any military presence in Syria, after Russia said Damascus' forces alone should control Syrian territory near the Israeli and Jordanian borders.
"Our position on Syria is clear," Israeli Prime Minister Benjamin Netanyahu told his parliamentary faction in broadcast remarks.
"We believe that there is no place for any Iranian military presence, anywhere in Syria."
