The two senior officials discussed the avenues of broadening security and defense cooperation after exchanging views on strategic issues of the region.
Assad's meeting with Maj.
Bagheri further reiterated that the Iranian nation and government will continue their support for Syria.
Shoigu noted that Iranian and Hezbollah forces have kept a distance from the border since the Russian military entered Syria, and so he considered the Israeli request was "exaggerated" and "superfluous", according to a report in Asharq al-Awsat.
He will also confer with the Syrian Defense Minister Fahd Jassem al-Freij during the trip.
But Israel seems adamant to drive the message home to Russian Federation that it will not tolerate an Iranian domination of Syria.More news: Why Toronto might not land Amazon HQ2, according to the mayor
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Prime Minister Benjamin Netanyahu, right, shakes hands with Russian Defense Minister Sergei Shoigu at a meeting in the former's office in Jerusalem on October 17, 2017.
Israeli Prime Minister Binyamin Netanyahu said Israel aims "to prevent Hezbollah or the Iranian forces from getting stronger in Syria, especially in obtaining sensitive weapons, and to prevent Iran from establishing military presence in general throughout Syria".
This week, the Israeli military said it attacked a Syrian anti-aircraft battery that had fired at its planes over Lebanon.
Following Monday's incident, Iran on Wednesday warned Israel it will not tolerate violations of Syrian sovereignty.
As the war in Syria seems to be winding down in Assad's favor due to Moscow's intervention, Israel fears that Iran will help Hezbollah produce accurate precision-guided missiles and aid Hezbollah and other Shi'ite militias to strengthen their foothold in the Golan Heights.
No one was hurt and no property damage was reported.