Mr Khamenei’s words were published on his official website on Wednesday, the day after a round of US sanctions were reimposed on Iran.
He said: “With regard to our situation do not be worried at all.
“Nobody can do anything.”
On Tuesday the US reimposed sanctions on Iran stopping it purchasing US dollars and some metals, as part of an effort to separate the country from the international financial system.
Another round of sanctions, targeting Iran’s oil and gas industries, will come into effect on November 4.
As part of the sanctions programme, non-US companies who do business with Iran may no longer be able to do deals with America.
Trump tweeted: “Anyone doing business with Iran will not be doing business with the United States.”
He also claimed the Iranian sanctions are: “the most biting sanctions ever imposed.”
Rudy Giuliani delivers his speech at the National Council of Resistance of Iran (NCRI) meeting
Iranian Foreign Minister Mohammad Javad Zarif told a state newspaper that the sanctions would not be successful.
He said: “If the Americans want to keep this simplistic and impossible idea in their minds they should also know its consequences.
“They can’t think Iran won’t export oil and others will export.”
China and Turkey have both said they will ignore any new US energy sanctions on Iran.
European countries have asked for their companies to be exempt from the sanctions in some sectors, but so far without success.
Trump announced he was pulling the US out of the Iran nuclear deal in May, claiming the country was not complying with the spirit of the deal and was continuing to back terror groups across the Middle East.
The decision was opposed by China, UK, France, Germany and Russia, who were also signatories to the Iran nuclear deal.
Last month Trump said he is prepared to meet Iranian leaders for talks “without preconditions”.