Velayati was also present at a meeting of top Iranian security officials in the city of Mashhad on August 14, 1993, where the decision to bomb the AMIA building is understood to have been made.
Trump and Putin are expected to discuss Iran's regional role and the Syrian conflict at a summit in Helsinki on July 16.
"I thanked President Trump for his support in responding to the appalling use of a nerve agent in Salisbury, after which he expelled 60 Russian intelligence officers", May said after talks with the USA leader at the Chequers residence in Buckinghamshire on Friday.
In a statement on Thursday, the Kremlin said the meeting between Putin and Velayati focused on regional security particularly the situation in Syria and the US withdrawal from the multinational nuclear deal with Iran. "They are trying to split our alliance".
Analysts say Trump is very eager to negotiate with Iran.
Some Iranian opposition figures and prominent expatriates have also called on Tehran to negotiate directly with Washington to resolve longstanding hostilities between the two nations.
"We do not want to negotiate with the Americans", he was quoted as saying by Russian news agencies. "Why would we trust them and hold negotiations with them?"
Iran has sought to shore up its alliance with Russian Federation as part of a diplomatic offensive to offset the effects of renewed USA sanctions.
Velayati said Tehran will simply cope with the sanctions like it has in the past.
Velayati and Russian officials on July 13 did not mention Argentina's request that Russia arrest and extradite Velayati to face charges in Buenos Aires in connection with the bombing of a Jewish community center in 1994 that killed 85 people.
US officials said in June they would push countries to reduce their Iranian oil imports to zero.
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.
They pointed to an extradition treaty between Russian Federation and Argentina that binds both countries to execute arrest warrants for wanted foreign nationals on the territory of either.
Commenting on a plan by the Trump administration to introduce sanctions against Iran's oil export, he said, "In spite of the sanctions, Iran sees no impediment to sell its oil".