Velayati is in Moscow to submit messages from Leader of the Islamic Revolution Ayatollah Ali Khamenei and President Hassan Rouhani to Russian President Vladimir Putin.
The presence of these issues, in the letters delivered to Putin, underscores the assertion by Tehran's embassy in Moscow that Velayati will meet the Russian energy minister after his meeting with Putin. The United States pulled out of a multinational deal in May to lift sanctions against Iran in return for curbs to its nuclear programme.
"Qassemi said after Trump's "strategic mistake" to exit the multilateral and global accord, Iran made a decision to dispatch a number of its special representatives" to other countries to "carry messages of high-ranking" Iranian officials about the country's viewpoints and stance on the "selfish" U.S. behavior which runs counter to worldwide regulations.
Tehran and Moscow already cooperate militarily in Syria, and have been instrumental in sustaining President Bashar al-Assad during the country's brutal seven-year civil war.
He said that after the US' withdrawal from Iran nuclear deal, also known as the Joint Comprehensive Plan of Action (JCPOA), which was a strategic mistake made by the U.S. president, the Islamic Republic of Iran chose to send special envoys to convey the messages of top Iranian leaders to other countries.
The meeting comes at a significant time for Iran.
Iran has also made moves to align closer with China, with Velayati expected to visit Beijing in the near future, Reuters reports.
Apart from the United States, the other signatories to the 2015 Iran nuclear deal - Russia, China, Germany, France and Britain - have said they still support the accord.
Velayati also said Iran and Russian Federation would "continue to cooperate in Syria", where both countries support President Bashar al-Assad's forces in the seven-year civil war there.
He added that cooperation in the region between the resistance front led by Iran and Russian Federation against terrorism and its supporters in Syria and other regional countries was indicative of an exemplary, strategic and long-term partnership between the two countries.
Russian President Vladimir Putin has received the Iranian leader's top adviser hours after conferring with the Israeli prime minister about Iran's presence in Syria.
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