Putin's spokesman, Dmitry Peskov, said that Velayati handed Putin letters from Khamenei and Iranian President Hassan Rouhani.
Argentina's government voiced its frustration with Russian President Vladimir Putin's administration on Thursday, after Moscow ignored a formal request from an Argentine judge to arrest a senior visiting Iranian official implicated in the 1994 bombing of the AMIA Jewish center in Buenos Aires.
Ali Akbar Velayati, Iran's Supreme Leader Ayatollah Ali Khamenei's top adviser on global affairs, smiles as he listens to questions from the media during a news conference after meeting with Lebanon's Prime Minister Tammam Salam at the government palace in Beirut May 18, 2015.
Velayati further quoted Putin as saying that "we don't accept the sanctions imposed by the United States and others against Iran".
Velayati told Iranian state television from Moscow that Khamenei "values improving ties with Russian Federation as a strategic partner" and that Moscow was "prepared to invest in Iran's oil sector".
"In these messages, our country's views and stances regarding the US' selfish and illegal behavior are explained to other countries", he said.
Both countries emphasized continuation of Astana talks between Iran, Russia and Turkey, he said.
Trump claims victory in North Atlantic Treaty Organisation spending dispute
Congress has taken a hard anti-Russia stance, almost unanimously approving past year a tough sanctions law targeting Moscow. They are also simplistic and crude - and based on Angela Merkel's cool reaction , it looks like they missed their mark.
Iran has also made moves to align closer with China, with Velayati expected to visit Beijing in the near future, Reuters reports.
Russian President Vladimir Putin greets Iranian regime envoy Ali Akbar Velayati in Moscow.
A US State Department official said this month that Washington's goal was to get as many countries as possible down to zero Iranian oil imports.
Argentina asked Russian Federation to arrest former Iranian foreign minister Ali Akbar Velayati for extradition in connection with the 1994 bombing of a Jewish centre in Buenos Aires, the foreign ministry said on Thursday.
He added that the 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.
Amir-Abollahian said Netanyahu was likely to ask for Putin's help to push Iran's military advisers out of Syria but added that this was an issue that could only be decided between Tehran and Damascus.
He also took a thinly veiled swipe at Donald Trump, saying the USA president's "unreliable" actions had made Iran's close ties with Moscow all the more necessary.