Khamenei addressed crowds during celebrations for Nowruz, the Persian new year, in the northeastern city of Mashhad. He warned Israel not to test Iran's patience.
"Israel's leaders sometimes threaten Iran but they know that if they do a damn thing, the Islamic Republic will raze Tel Aviv and Haifa to the ground," he was quoted by Iran's state-funded broadcaster Press TV as saying.
Khamenei added that Iran's adversaries were working through economic channels to undermine the country's reputation, adding the "center of conspiracy and the basis of hostility with the Iranian nation is the U.S. government."
Obama expressed concern about Israeli settlement activity and the role of Hamas but said direct negotiations between Israeli and Palestinian leaders could bring about peace. He added his support for an "independent, viable and contiguous Palestinian state."
Obama added there were "unbreakable bonds" between the U.S. and Israeli governments.