"We believe that there is no room for any Iranian military presence anywhere in Syria", he said.
Prime Minister Benjamin Netanyahu also said in remarks to the Knesset on Monday that Iran should be pressured to leave Syria altogether.
The secret agreement was hashed out over the phone between the Russian Defense Minister Sergei Shoigu and his Israeli counterpart Avigdor Lieberman.
The United States, Russia, and Jordan agreed past year to include Daraa in a "de-escalation zone" and freeze the lines of conflict there.
After liberating the entirety of Damascus city and the broader province from an array of hardline Islamist militant groups, including the Daesh* terrorist group, the Syrian Army and other government forces are set to launch a major offensive in southern Syria, near the Arab Republic's border with Israel.
Donald Trump says summit with Kim Jong Un still on the cards
At that meeting, they declared they would work toward a nuclear-free Korean peninsula and a formal end to the 1950-53 Korean War. Trump said in a letter to Kim on Thursday he was cancelling the planned Singapore summit, citing North Korea's "open hostility".
Russian Federation and Israel have allegedly agreed that militias loyal to Iran will be held back so that Assad can retake the region from rebels. In this endeavour it has formidable obstacles to overcome: "the regime is more dependent than ever on Iran, which Israel regards as its most implacable state foe; other enemies, particularly Hizbollah and Iran-backed Shiite militias, are entrenched in Syria with Russia's blessing; and the US, notwithstanding the Trump administration's strident rhetoric, has done little to reverse Iran's gains", reads a February report from the International Crisis Group. It stressed that the Syrian army was determined to retake all parts of Syria.
According to the report, the understandings were reached in a series of indirect meetings in Jordan, where Iranian officials, including the envoy to Jordan, met with top Jordanian officials, who in turn met with senior Israeli security officials.. Israel suspects Syria's ally Iran of seeking to establish a military presence close to territory it controls and has repeatedly struck Syrian and Iranian targets in Syria when it felt threatened. The report said a Jordanian mediator carried messages between the sides.
Following Lavrov's statement, the Israeli PM asserted that there is no place for Iran's military forces in Syria.