"The Secretary-General is dismayed by the remarks threatening Israel's existence attributed over the last two days to the Supreme Leader and the President of the Islamic Republic of Iran," the U.N. press office said. "The Secretary-General condemns these offensive and inflammatory statements."
"(Ban) believes that all leaders in the region should use their voices at this time to lower, rather than to escalate, tensions," it said in a statement.
"In accordance with the United Nations Charter, all members must refrain from the threat or use of force against the territorial integrity or political independence of any state."
Earlier this week Iranian media reported that Iran's Supreme Leader Ayatollah Ali Khamenei said Israel would one day be returned to the Palestinian nation and would cease to exist.
The Iranian remarks came on the heels of a series of Israeli media reports suggesting that Israel could attack Iranian nuclear facilities ahead of U.S. presidential elections in November.
Israel, the United States and their allies in Europe and elsewhere believe Iran is developing atomic weapons, a charge Tehran denies.
(Reporting by Louis Charbonneau; Editing by Jackie Frank)