Russian President Vladimir Putin and Israeli Prime Minister Naftali Bennett agreed that Israel's policy toward Syria, including airstrikes, would continue, said Israeli Construction and Housing Minister Zeev Elkin.
Elkin, who acted as a translator between Putin and Bennet, said that the meeting was "exceptionally warm."
Also, an Israeli air force senior officer said that the leaders agreed to work to remove Iran from Syria.
The Jerusalem Post reported that the recent Russian-Israeli rapprochement, represented in the meeting between Putin and Bennett and the understandings they reached, is because they "are seeking to remove Iran and its proxy Hezbollah from the country [Syria]."
For nearly a decade, Israel has been working on the "difficult task of destroying Tehran's dreams of regional hegemony and a forward base" against Israel with hundreds of airstrikes in Syria.
Sources told the newspaper that Israel and Russia have been using a "deconfliction mechanism to avoid an unwanted conflict," Moscow has allowed Tel Aviv to maintain its freedom of operation over Syria, as long as it does not endanger their forces.
They explained that the US, Israel's strongest ally, does not object to the Israeli-Russian understanding.
Washington believes it can lead to rapprochement with Moscow, which is the key influencer in the Middle East, and President Bashar al-Assad will listen to Moscow when he wants to gain anything from the outside world.
In light of international efforts to reach a settlement in Syria that would allow the war-torn country to begin reconstruction, Moscow is aware that the process requires the removal of all foreign forces, especially Iran and its proxies from Syria.
"The question is: Will Assad listen to Putin and choose Russian influence over Tehran? Or will he decide to stay in Iran's camp and allow the Islamic Republic to entrench its forces and weapons even further for a future war with Israel?" concluded the newspaper.
Political sources in Tel Aviv revealed earlier that Putin and Bennett reached new understandings in their meeting in Sochi, including resolving the dispute over the Israeli raids on Iranian sites established by the Iranian Revolutionary Guards Corps (IRGC) and its militias.
Russia accused Israel of carrying out "unnecessary raids" and demanded to be informed ahead of time, warning that strikes on Russian sites sabotage Moscow's efforts to establish stability.
However, Bennett pledged to give the Russians accurate information about any raids and ahead of time.
He also vowed that the strikes would become more localized and would not target the infrastructure of the Syrian regime.
They agreed to keep the Lebanese Hezbollah militia and other militias affiliated with Iran as far as possible from the Israeli borders.