A U.S. State Department official said this month that Washington's goal was to get as many countries as possible down to zero Iranian oil imports. However, Secretary of State Mike Pompeo said on Tuesday the United States might consider requests from some countries to be exempted from sanctions.
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.
But European firms are reluctant to risk far-reaching U.S. financial penalties they would face for doing business in Iran.
Israeli Prime Minister Benjamin Netanyahu, who views Iran as Israel's arch-enemy and strongly backs Trump's decision to quit the nuclear deal, was also visiting Moscow on Wednesday.
Asked about Netanyahu's visit, Velayati said: "His presence or absence in Russia has no effect on our strategic mission in Moscow."
Israel is concerned that Iran is establishing a military presence in neighbouring Syria and it has attacked Iranian targets there.
Velayati is also expected to visit China in the near future, Iran's foreign ministry said on Tuesday.
