BBC News
In a rare rebuke, Mr Annan reminded Iran that, as a UN signatory, it had undertaken not to threaten the use of force against another state.
While President Mahmoud Ahmadinejad’s words provoked international outrage, Tehran said the West was over-reacting.
Israel has called for Iran to be expelled from the UN.
A statement released by the UN said the secretary general “read with dismay the remarks about Israel attributed to Mr Mahmoud Ahmadinejad”.
It is rare for Kofi Annan to publicly rebuke a UN member state, says the BBC’s Laura Trevelyan in New York.
Our correspondent says Mr Annan, like other secretaries general, sees himself as the servant of the 191 countries that make up the UN.
Israeli demand
Mr Ahmadinejad made his comments at a conference on Wednesday in Tehran entitled The World without Zionism.
Referring to Iran’s late revolutionary leader Ayatollah Ruhollah Khomeini, Mr Ahmadinejad said: “As the imam said, Israel must be wiped off the map.”
Mr Ahmadinejad’s speech drew a chorus of global condemnation, not least from Israel, which called for Iran to be kicked out of the UN.
“We must submit a clear-cut request to the UN secretary general and the Security Council to obtain Iran’s expulsion from the United Nations,” Israeli Deputy Prime Minister Shimon Peres said.
Correspondents say it is unlikely that such a request would be followed through.
British Prime Minister Tony Blair expressed “revulsion” at Mr Ahmadinejad’s words, which he called “completely and totally unacceptable.”
“Can you imagine a state like that with an attitude like that having a nuclear weapon?” he said.
Negotiations have stalled between the EU and Iran over attempts to persuade Tehran to abandon its nuclear ambitions.
In Washington, White House spokesman Scott McClellan said the Iranian leader’s words underlined US concerns about Tehran’s nuclear programme.
The US suspects Iran of wanting to acquire atomic weapons but Tehran insists its nuclear programme is for peaceful purposes.
‘Over-reacting’
French President Jacques Chirac said Iran was at risk of becoming “an outlaw state”.
“I was profoundly shocked by the statements of the Iranian president, which are totally senseless and irresponsible,” he said.
Russian Foreign Minister Sergei Lavrov, on a visit to Israel, called Mr Ahmadinejad’s comments unacceptable.
He said they gave ammunition to those seeking to refer Iran to the UN Security Council over its nuclear policy.
Russia is seen as a supporter of Iran in the international row over its nuclear programme.
But the mood in Tehran seems defiant, says the BBC’s diplomatic correspondent, Bridget Kendall.
She says officials there played down their president’s comments as nothing out of the ordinary.
Instead, our correspondent says they accused the West of deliberately over-reacting in an attempt to smear Iran’s image abroad and bolster their claim that Iran might be seeking nuclear weapons.
