Greeting Netanyahu at the start of their Kremlin negotiations, Putin emphasized a high level of trust between them. Netanyahu's visit to Moscow follows his talks last month with US President Donald Trump.
Netanyahu praised Russia's role in fighting the Islamic State group and other radical militants in Syria. At the same time, he raised strong concern about the presence of Iranian and Hezbollah forces in Syria.
"One of the things that we are fighting together is radical Islamic terrorism," Netanyahu said as he and Putin sat down for talks.
"Russia has made a very important contribution. Naturally, we do not want this terrorism to be replaced by the radical Shiite Islamic terrorism led by Iran."
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Russia has sided with Iran and Hezbollah in helping support Syrian President Bashar Assad, but at the same time it has maintained warm ties with Israel. The two nations have coordinated their actions to prevent any possible incidents between their militaries in Syria.
Before the talks, Putin's spokesman Dmitry Peskov denied media reports that Moscow has given Israel a green light to strike Hezbollah.
"It has nothing to do with reality," Peskov said in a conference call with reporters. "It hasn't been discussed, and there is no talk about it.