Shimon Peres, the Israeli deputy prime minister, did not mention the Iranian president directly, but he said on Tuesday: "I am simply saying, with regards to those threats, that those who issue threats can themselves be threatened.
"Those who threaten destruction risk being destroyed themselves."
Iran says that its nuclear work is designed only for energy purposes, but Israel and Western powers say that it is a front to develop nuclear weapons.
The UN meeting overnight did not yield any results, with China and Russia still resisting sanctions.
Israel has come to view Iran as its chief enemy since the downfall of Saddam Hussein in Iraq in 2003. Israel bombed a nuclear reactor in Iraq in 1981.
Israel has grown increasingly alarmed by Ahmadinejad's suggestion that Israel be erased from the map, as well as his dismissal of the Holocaust as a myth.
Although it refuses to confirm that it possesses nuclear weapons, Israel is widely thought to have at least 200 atomic warheads, making it the only nuclear power in the Middle East.
Israel's foreign minister, Tzipi Livni, urged other countries to take Ahmadinejad's comments seriously.
"The Jewish people's experience has shown that even the most extreme threats could be realised, and the international community should therefore not ignore the threats and statements of Iran's president," Livni said on Monday.