Araghchi's statement came in an interview with the American broadcaster NBC and its influential weekly program Meet the Press.
The high-profile foreign minister has often represented Iran internationally and led Iranian delegations in negotiations.
After the outbreak of war, Araghchi has been less visible, but on Sunday he appeared in an interview with NBC - and offered a greeting to the Trump administration:
We will not allow anyone to interfere in our internal affairs. It is up to Iran to choose a new leader.
He also said Trump "should apologize to the people of the region and Iran for the killing and destruction that has occurred."
