Ban criticised the Iranian comments as against the UN charter
UN chief Ban Ki-moon has said he was "shocked and dismayed" at recent comments by Iranian President Mahmoud Ahmadinejad about Israel.
Iran's official news agency reported Mr Ahmadinejad saying that the world would soon see Israel's destruction.
He said the war between Israel and Hezbollah in 2006 showed for the first time Israel's weakness.
The Iranian leader is a outspoken critic of Israel and has said the Holocaust of European Jewry is a myth.
"The secretary-general points out that the state of Israel is a full and longstanding member of the United Nations with the same rights and obligations as every other member," the UN statement read.
"Under the United Nations Charter, all members have undertaken to refrain from the threat or use of force against the territorial integrity or political independence of any state."
Mr Ahmadinejad was quoted by Irna, the official Iranian news agency, as saying: "The hegemony of the occupier regime [Israel] had collapsed, and the Lebanese nation pushed the button to begin counting the days until the destruction of the Zionist regime."
"God willing, in the near future we will witness the destruction of the corrupt occupier regime," Mr Ahmadinejad said.
In October 2005, the Iranian president made a statement in which he envisaged the replacement of Israel with a Palestinian state. This was widely translated as a call for Israel to be "wiped off the map".
While he has repeated similar comments many times, he has insisted that Iran is not a threat to Israel.
Israel failed to achieve its stated aims in the war with Hezbollah last year.
An Israeli inquiry into the war concluded in April that Israel's political and military leaders were guilty of "very serious failings" in handling the war.