(CNN) With Russia apparently beefing up its military presence in Syria , some countries are getting nervous about what could happen -- including Israel .

Israeli Prime Minister Benjamin Netanyahu visited Russian President Vladimir Putin on Monday to discuss "the Middle East peace process and the fight against the global terrorist threat," the Kremlin said

But in a rare move, Netanyahu brought several top Israeli military and security officials with him to Moscow.

Israel Defense Forces Chief of Staff Lt. Gen. Gadi Eizenkot, IDF Director of Military Intelligence Maj. Gen. Hertzi HaLevi and National Security Adviser Yossi Cohen accompanied the Prime Minster, Netanyahu's office said.

The meeting, which was closed to the media, came after satellite pictures showed a rapid buildup of an air force base in Syria, with loads of Russian military equipment moving in. Among the Russian equipment are advanced Russian Sukhoi Flanker fighter jets.

Afterward, Netanyahu called the talks "substantive" -- noting that both countries had agreed to "a joint mechanism for preventing misunderstandings between our forces" in and around Syria.

He said there was a "very big" need to prevent such "misunderstandings."

"Israel is constantly working to prevent the transfer of advanced and deadly weaponry from Syrian territory to Hezbollah," said Netanyahu, who also alluded to a threat from the Golan Heights.

"Israel is taking action and, when it does so, it is important for everyone -- including Russia -- to know that we are taking action."

Analyst's take

The cause for Israel's concern "relates to the provision by Russia of weapons systems to some of Israel's most determined enemies," said Middle East analyst Jonathan Spyer at the Global Research in International Affairs Center.

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Russian Defense Minister Sergei Shoygu has said the recent Russian military buildup in Syria is "defensive in nature" and aimed at supporting Russian obligations to Syrian President Bashar al-Assad's regime. Russia has been a staunch ally of Syria, even as much of the world decries al-Assad's role in the country's gruesome civil war.

Israel's policy has been to stay out of the Syrian civil war , which is raging nearby, right across the Golan frontier. But Israel says it has established red lines, such as making sure advanced military equipment such as Russian anti-aircraft missiles don't fall into the hands of Hezbollah in Lebanon or other militant groups.

It's also about issues that go beyond the civil war and to groups and efforts that threaten more directly.

According to Netanyahu, the Syrian government -- the same one that's getting Russian weaponry -- has been involved by arming Hezbollah and working with Iran to try to "build a second terrorist front against us from the Golan Heights."

Putin: Russia's actions 'will always be very responsible'

"Israel has been, in the course of the last four years, determined to prevent the provision of certain weapon systems from Syria to Hezbollah," Spyer said.

"And to achieve that, Israel has required complete air control -- master of Syria's skies to operate when and where it wants -- anywhere over the skies of Syria."

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And while Israeli and Russian forces aren't necessarily on a collision course, they want to make sure no inadvertent collisions occur.

To this point, Putin insisted Monday that "all of Russia's actions in the region will always be very responsible."

"We are aware of the shelling against Israel and we condemn all such shelling," the Russian leader said. "In regard to Syria, we know that the Syrian army is in a situation such that it is incapable of opening a new front. Our main goal is to defend the Syrian state."

Israel's not alone in its concerns about increased Russian military force in Syria.

The United States has been at odds with Russia over Syria since the civil war started. U.S. leaders have said al-Assad must leave office after frequent attacks against civilians and the use of chemical weapons . But Russia, a close ally of al-Assad's, continues supporting the Syrian regime.

The U.S. has also been launching airstrikes to fight ISIS in Syria, and it now wants to avoid accidental military encounters with Russian forces in the country.

At a news conference Wednesday, U.S. Secretary of State John Kerry told CNN's Elise Labott that his Russian counterpart, Sergey Lavrov, has assured him that Russian activities in Syria are aimed at fighting ISIS. But Kerry said he isn't taking those assurances "at face value," given the Russian military assets being moved into Syria.