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.
"We co-ordinate the Iranian presence in Syria with Russian Federation and Syria", Mr Velayati said during a meeting at Moscow's Valdai Club discussion platform.
Velayati also said that U.S. sanctions against Iran could raise oil prices and harm oil consumers.
He referred to the USA demand for Iran's exit from Syria and Iraq. Israel seized Syria's Golan Heights without global recognition in a 1967 war and retained it after a second conflict ended in a 1974 truce, which left the countries at an indefinite standoff that has witnessed a resurgence in violence in recent months. During the interview, Velayati disclosed that a Russian oil company recently signed a $4 billion contract with Iran's Ministry of Oil.
Under the 2015 agreement, Iran strictly limited uranium enrichment capacity to satisfy the powers that it could not be used to develop atomic bombs.
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I don't trust Russian Federation to police Iran or anyone else in Syria.
Israeli Prime Minister Benjamin Netanyahu also met with Putin in Moscow on Wednesday when he discussed Israel's demands for a withdrawal of Iranian forces from Syria, where they are helping the regime battle rebels in a civil war. "We will immediately leave if Iraqi and Syrian governments want it, not because of Israel and America's pressure", Velayati stated. "We will deal with the American presence from Syria to Iraq, Lebanon, Yemen and north Africa".
Trump said at a news conference in Brussels on July 12: "I know they're having a lot of problems and their economy is collapsing".
Israel also said it carried out several strikes on Iranian forces in Syria this year in response to Iranian rocket fire and an Iranian drone infiltration from Syrian territory.
The Bubble, an online Latin American news site, reported that Moscow avoided responding to the extradition request before Velayati left the country for meetings in Beijing on July 13, out of deference to Iran's "strategic partnership" with Russian Federation in Syria and elsewhere.