Velayati, former Iranian foreign minister and incumbent global adviser to Iran's Supreme Leader Ayatollah Ali Khamenei, travelled to Moscow on Wednesday to convey messages from Khamenei and Iranian President Hassan Rouhani to Putin.
"Iran and Russian Federation are diametrically opposed to US, NATO or any other countries' presence around the Caspian Sea region", he said.
Israel worries that Assad could let his Iranian and Lebanese Hezbollah reinforcements entrench near Israeli lines, or that Syrian forces may defy a 1974 Golan disengagement agreement.
Israel is anxious about the presence of Iran, ally of Syrian President Bashar al-Assad's regime, in Syria, and demands all Iranian forces completely withdraw from the war-torn country.
Iran and Russian Federation back Syrian President Bashar al-Assad in the country's civil war.
"The relationship between Iran and the Russian Federation is a strategic relationship and in recent years the collective bilaterial and regional relations have expanded", Iran's ISNA news agency quoted Velayati as saying on arrival in Moscow.
The high-level talks precede Monday's summit in Helsinki between Mr Putin and US President Donald Trump, who are set to discuss the Iranian presence in Syria.
Velayati was apparently referring to Trump's decision in May to withdraw from Iran's 2015 nuclear agreement with world powers, a move that triggered the reinstatement of US sanctions.
Hours later, the Israeli military said it "targeted three military posts in Syria in response to the infiltration of the Syrian UAV into Israel that was intercepted by the IDF earlier today", along with another video purported to show one of the strikes.
Russian Federation has publicly called for the withdrawal of Iranian troops from a post-war Syria but can not guarantee Iranian compliance.
"A public deal that accepts Assad in return for limiting Iranian influence implicitly if not explicitly gives him some legitimacy", Kamel said.