Netanyahu noted that Israel would not tolerate a military establishment of Iran and its proxies in any area of Syria for many times.
Alexander Lavrentiev, Putin's special presidential envoy to Syria and a senior member of the Russian negotiating team at last Monday's Putin-Trump summit in Helsinki, arrived in Tehran to discuss the implications of the summit for Iran's military presence in Syria, Iranian news outlets reported.
In a late night Twitter message directed at Rouhani, Trump warned him to "never, never, ever threaten the United States again" or "suffer consequences the likes of which few throughout history have ever suffered before".
The Russian delegation visited Netanyahu's residence Monday evening.
Israeli jets reportedly struck an Iranian-supervised military facility in northwest Syria that in the past allegedly was used to produce chemical weapons including sarin gas.
"Iran is not a country you can push", he said in an interview with Russia's Kommersant daily, adding that exerting pressure on Iran is entirely unconstructive and that Moscow by no means agrees to Washington's unilateral sanctions against Tehran.
The Russian ambassador made the remarks in an interview with Russian newspaper Kommersant, during which he also pointed to Russia's attempts to bring under control a possible military confrontation between Iran and the Israeli regime in Syria.
A series of strikes that have killed Iranians in Syria have been attributed to Israel.
He said the Russian government's determination to continue joint work to combat terror has not been undermined, and the two countries will continue to move on the same path until stability and security are fully restored to Syria.
Smoke following the explosions in Syria is seen from the Israeli-occupied Golan Heights near the Israeli Syrian border, July 19, 2018.
Israel is eager to obtain guarantees that Iranian forces and allied groups, such as Hezbollah, will be kept away from the Golan.
Jordan's foreign ministry announced in a statement that the kingdom received 422 Syrian citizens, after earlier saying it had given permission for 800 to arrive.