Shoigu said S-300 missiles will strongly strengthen combat capabilities of the Syrian air defense due to their jamming invulnerability and firing speed.
Shoigu said the supply of S-300s to Syria will "calm down some hotheads" whose actions "pose a threat to our troops".
President Trump's top advisor on national security matters also reiterated his warning that any future chemical weapons attack attributed to the Syrian military - a basis already cited twice for recent U.S. airstrikes on Syria - would be met with a harsh response.
Putin and Syrian President Bashar al-Assad discussed the additional measures and delivery of the S-300 system on the phone Monday, the Kremlin said. "And it's not our fault" Shoigu said.
Peskov said the measures were "not directed against third countries but towards defending our own military".
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Israel's former Military Intelligence chief Amos Yadlin, who now heads the influential Institute for National Security Studies in Tel Aviv, said he assumed the air force would work quickly to destroy the S-300, if it were indeed handed over to Syria. Russian officials say Syria's outdated S-200 systems aren't sophisticated enough to identify the Russian plane as a friendly one.
Russian President Vladimir Putin looks through the porthole while aboard the presidential plane on December 11, 2017, during the approach to the Russian air base in Hmeimim in the northwestern Syrian province of Latakia.
Russian Federation already has its own S-300 air defense system in Syria, along with the more advanced S-400 system. An Israeli military delegation travelled to Moscow last week to share information about the incident.
According to the statement, Putin reiterated that Russia holds Israel responsible for the downing of the Russian plane.
"The Russian side proceeds from the fact that the actions by the Israeli air force were the main reason for the tragedy", a statement said. Russian Federation has blamed Israel, whose military was conducting airstrikes on Syria at the time, for the incident.
Earlier on Sunday, the Russian defense ministry released the findings of its investigation into the downing of the plane and the deaths of the crew.
Meanwhile, the Kremlin on Monday accused Israeli pilots of acting deliberately and said the downing of the Russian plane would harm relations between the two countries.