Tel Aviv had earlier claimed that their planes had already returned to Israeli airspace at the moment of the incident.
The Israeli leader said that Israel "has been very successful" in the last three years in preventing Iran's military buildup in Syria as well as its attempts to deliver lethal weapons to Hezbollah in Lebanon.
Israel is still expressing its "deep regret" over the loss of the crew of the Russian plane that was shot down last week by Syria during the IAF air strike over Latakia and its condolences to the families of the air crew in Russia and the Russian people as a whole.
Netanyahu told Putin Israel was sticking by its version of events and "reiterated that the Syrian military, which brought down the plane, and Iran, whose aggression is undermining stability, are responsible for the unfortunate incident", the statement said.
The United States is also urging Russian Federation to reconsider.
Netanyahu spoke by telephone with Russian President Vladimir Putin on Monday.
Russia supplying Syria with the S-300 missile complex is a measure to protect Russian troops and is not directed against third countries, Russian presidential spokesman Dmitry Peskov said in reply to the question about whether Russia supplying S-300 missiles to Syria can damage Russian-Israeli relations.
Russian Federation launched its campaign in Syria to support President Bashar al-Assad in 2015 and though the involvement turned the tide of war in favour of Syrian government forces, Moscow has since played a careful balancing act, maintaining good ties both with Iran and Israel.
Concurrently, US National Security Adviser John Bolton said Russia's decision was a "major mistake" that would cause a "significant escalation" of tensions.
"We're not going to leave as long as Iranian troops are outside Iranian borders and that includes Iranian proxies and militias", Bolton said.
Shortly before the downing, Israeli strikes had hit targets inside Syria, reportedly preventing an arms shipment to the Iranian-backed militant Hezbollah group.
The incident comes a day after the opposition group announced rejecting to cooperate with the Russian-Turkish agreement. Gen. Igor Konashenkov produced data that he said had been collected by Russian air defense systems in Syria purportedly indicating that one of the Israeli F-16 fighter jets was flying close to the much larger Russian plane.
Russian Defence Minister Sergei Shoigu. "Today the situation has changed, and through no fault of ours", he stressed.
However, Syria's Ambassador to Russia Riyad Haddad said following the announcement that Damascus required the S-300 "in order to defend Syrian land from Israel's aggressive actions".
Russian officials said Syria's Soviet-made S-200 systems, one of which downed the Russian plane, weren't sophisticated enough to identify the Russian aircraft as a friendly one.