This very open clash of the two leaders comes after a report by the International Atomic Energy Agency that expresses continued concern about Iran's possible involvement in planning for nuclear weapons.
Olmert used a speech to a pro-Israel lobby group in Washington to call for the international community to stop the Iranian nuclear threat "by all possible means."
Olmert told the American Israel Public Affairs Committee (AIPAC) on June 3 that countries should penalize Iran by imposing stringent sanctions, in addition to the relatively mild sanctions already placed on Iran by the UN Security Council for refusing to abandon uranium enrichment.
"International, economic, and political sanctions on Iran, as crucial as they may be, are only an initial step and must be dramatically increased," Olmert said. "Iran's defiance of international resolutions and its continued tactics of deception and denial leave no doubt as to the urgent need for more drastic and robust measures."
The Israeli leader listed possible actions like barring business travelers, blocking financial transactions, and impeding Iran's import of refined gasoline. He said every country must understand that the long-term cost of a nuclear Iran greatly outweighs the short-term benefits of doing business with Iran.
Iran has steadfastly denied it is seeking nuclear weapons and says its nuclear program is for civilian energy generation only.
Meanwhile, Ahmadinejad told journalists on the sidelines of a world food summit in Rome that Israel will eventually disappear, with or without Iranian involvement.
"We think that all oppressors and occupiers agree with us," he said. "This will happen whether we are involved in it or not, and Europe will certainly benefit from this."
He said Europe is bearing the economic and political costs of what he called the "false regime" of Zionists.