"I believe the international efforts will achieve the goals," Olmert said. "There is no need to get caught up in any apocalyptic prophecies that have no basis in reality."
He warned against panic over Iran's nuclear program, telling Israel Radio that, "Iran is far from crossing the nuclear threshold ... Unfortunately, it is not as far as I would like it to be but it is also not as close as it proclaims to be."
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Israeli concerns have been heightened by Iranian President Mahmoud Ahmadinejad's repeated calls for Israel's destruction. Olmert has never ruled out taking military action, but he has repeatedly said he would prefer a diplomatic solution.
The U.N. Security Council imposed limited sanctions in December and strengthened them slightly last month because of Iran's refusal to suspend uranium enrichment, which can produce fissile material for a weapon or fuel for civilian energy. The council has set a new, late May deadline.
"The security council has passed two resolutions, which impose unprecedented sanctions," Olmert said. "I think there is a possibility, even without a military operation, to stop Iran from going nuclear."
Olmert also said that last summer's war against Hezbollah guerrillas in south Lebanon was painful but succeeded in changing "the rules of the game" in the region.
"The threat is not as it has been for many many years. At this moment the northern border is totally quiet," he said. "The main goal we wanted to achieve, changing the equation, I think it was achieved but at a very heavy price."
He said the time would not be ripe for peace negotiations with Syria until Syrian President Bashar Assad stopped supporting Palestinian militants.
"We want to have peace with every Arab state, including Syria," he said. "But ... it is not enough to say publicly 'I want peace,' you have to act on this."
The prime minister traditionally grants Israeli media outlets two sweeping interviews a year, one in the fall, ahead of the Jewish New Year, and another prior to Independence Day, which begins Monday evening.
Complete coverage is available in FOXNews.com's Mideast Center.