Velayati is in Moscow in a bid to submit messages from Leader of the Islamic Revolution Ayatollah Seyed Ali Khamenei and also President Hassan Rouhani to Russian President Vladimir Putin, according to Iranian Foreign Ministry Spokesman Bahram Qassemi.
Iranian Foreign Ministry Spokesman Bahram Qassemi said on Tuesday that Velayati's visit was part of efforts to make Iran's stance clear after the United States pullout from the JCPOA signed between Tehran and the P5+1 group of countries in 2015.
The two countries fought their last direct war in 1973, which formally ended with the signing of separation agreements in their not-yet-finalized borders in the Golan Heights.
Iran describes its military support for Syrian President Bashar al-Assad and Iranian-allied militant groups in Syria as part of an "axis of resistance" against Israel, whose destruction Tehran long has called for.
A full withdrawal of Iranian-backed forces from Syria is a virtual non-starter.
The military said it will "continue to operate determinedly and decisively against any attempt to breach Israeli sovereignty and will act against any attempt to hurt its civilians".
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Iran and Russian Federation back Syrian President Bashar al-Assad in the country's civil war.
The meeting comes at a significant time for Iran.
A possible deal could see Syrian troops replacing Iranian forces and its proxy Hezbollah militia in the areas near the Israeli-occupied Golan Heights.
"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.
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 USA sanctions.
Moscow, however, may have enough leverage over Tehran to persuade it to diminish its footprint, stay away from the frontier with Israel and perhaps reduce the number of bases, missile factories and advisers it maintains in the country - especially if the terms are not publicized and they come with other guarantees.
The IDF also said it "holds the Syrian regime accountable for the actions carried out in its territory and warns against further actions against Israeli forces".