After meeting with his Jordanian counterpart, Lavrov said that Iran is one of the key powers in the region, and that it would be "absolutely unrealistic" to expect it to abandon its interests.
He said regional powers should discuss mutual complaints and negotiate a compromise.
Russia and Iran have provided crucial military support to Syrian President Bashar Assad's forces, helping them turn the tide in the civil war.
Israel has said it will not tolerate an Iranian military presence in Syria and has launched military strikes against Iranian targets there in recent months.
Lavrov said Russian President Vladimir Putin and US President Donald Trump would discuss the situation in southern Syria, where government forces are waging a new offensive, at their July 16 summit.
He said a cease-fire in the region brokered by Russia, Jordan and the US had envisioned the withdrawal of non-Syrian forces and the deployment of Syrian troops along the frontier with Israel.