Meanwhile, a delegation of the U.S. National Security Council has arrived in Israel for a meeting with Israeli counterparts on Tuesday that will focus on Iran and the situation in southern Syria.
The agreement, announced in a joint US-Russian statement Saturday, affirms a call for "the reduction, and ultimate elimination" of foreign fighters from southern Syria.
Lavrov, who was quoted by RIA news agency, denied comments made by senior United States officials that the recently announced ceasefire agreement in southern Syria included a Russian commitment to ensure that Iranian-backed militias would be withdrawn from the country.
While the agreement requires all foreign forces - including Iranian troops and those backed by Tehran - to leave Syria, the deal does not set deadlines for their departure.
But according to an unnamed Israeli official, under the deal, militias associated with Iran would be allowed to maintain positions as close as five to seven kilometers (3.1-4.3 miles) to the border in some areas, Reuters reported Monday.
The presence of Iran in Syria is legitimate, Lavrov was quoted as saying by another agency, Interfax.
Yet, the source continued that Israel shows concern over the absence of a timeline in the agreement, and the fact that secret agreements among parties can only guarantee distancing Iranians and militias to relatively short distance from the Israeli border at Golan.
Israeli Cabinet Minister Tzachi Hanegbi said Sunday that the agreement "does not answer Israel's unequivocal demands that there will be no developments that bring Iranian or Hezbollah forces closer to Israel's border with Syria in the north". Gadi Eisenkot secretly flew to Brussels on Friday where he met with met with the head of the US Army's European Command Gen. Curtis Scaparrotti.
Describing Israel's security policy as the "right combination of firmness and responsibility", Netanyahu said Monday that he has "informed our friends in Washington and our friends in Moscow that we will operate in Syria, including southern Syria, in accordance with our understanding and in accordance with our security needs".
Netanyahu has warned that Iran plans to create a permanent presence in the country, including with naval and air force bases, and that Israel will not allow it to happen.