"Our policy towards the United States is clearly set and does not change with the movement of individuals. It does not matter to us who comes and goes," Khamenei said in a speech carried live on state TV.
Khamenei was speaking on the anniversary of the 1979 seizure of the U.S. embassy in Tehran, which coincided with the birthday of Islam's Prophet Mohammed.
There have been no U.S.-Iranian diplomatic relations since the seizure.
The Democratic nominee, Joe Biden, has pledged to rejoin Iran's 2015 nuclear deal with six powers if Iran returns to compliance with it.
In 2018 President Donald Trump abandoned the deal, under which international financial sanctions on Iran were lifted in return for curbs to its nuclear program. Iran followed Washington's rejection by reducing its compliance.