The world marked the third anniversary this week of the US's invasion of Iraq and the day columns of tanks entered Baghdad to topple Saddam Hussein's regime. But once triumphed as the beginning of a new world order, the invasion may have had the opposite effect, former senior Israeli officials said Monday. With the US stuck and focused on its troubles in Iraq, the superpower might have missed out on its opportunity to stop Iran's nuclear program, leaving Israel to deal with the threat alone, they warned. "We cannot let this war prevent action against Iran," warned Maj.-Gen. (res.) Uzi Dayan - Prime Minister Ariel Sharon's former national security adviser. In 2002 - before the war - Dayan said he told the Bush administration it was making a mistake by invading Iraq. "They should have already then dealt with Iran. Now we can only hope they get out of Iraq and are still able to take action against Iran," he said. Backing Dayan's concern regarding America's ability to act against Iran while stuck in Iraqi mud, Prof. Uzi Arad - a former Mossad official and the founding head of the Institute for Policy and Strategy at the Interdisciplinary Center in Herzliya - said Israel was also at fault for the US's wrong list of priorities. While America originally thought the war in Iraq would empower it to deal with Iran, it in fact had the opposite effect, Arad said. Israel, he added, also had high hopes for the war in Iraq but all of those had similarly disappeared. "Israel hoped Iraq would turn pro-Western, would prosper and would become another country that supported peace with Israel," said Arad, who also served as foreign policy adviser to former prime minister Binyamin Netanyahu. "We thought it [the war] would be able to serve as an example of what democratization can do in the Middle East." Israel and the US, Arad said, were "caught up in a wrong set of priorities" and instead of invading Iraq and disengaging from the Gaza Strip, the countries should have invested their efforts in curbing Iran's race for nuclear power. "There is no reason why Iran could not have been referred to the United Nations Security Council a year or two ago before it was at the stage of enriching its uranium like it is now," he said. But instead of focusing on Iran, Arad said, Sharon decided to invest billions of dollars and all of Israel's resources in evacuating Gaza - a move he could have made several years later. The US also missed the boat and during the critical years in which there was a chance to stop Iran, US President George W. Bush got caught up in Iraq, he said. "We are now paying the price for these mistakes," Arad claimed. "And while the US is trying to improve its ability to act against Iran, it might be too little too late." But both officials admitted that the war in Iraq also brought positive changes to the Middle East; Libya abandoned an advanced nuclear project and joined Egypt, Jordan and Morocco as Arab countries that supported stability in the region. "There was the fall of Saddam and the impact it had on Libya," Arad said. "But there were hopes for a better outcome and the US never thought it would be stuck there for three years and that the war would be highly unpopular." The war on Iraq and its prolongation, the analysts said, was also partially responsible for Hamas's victory in the recent Palestinian elections. The US, Arad said, should not have pressured the Palestinian leadership to hold elections until they dismantled the terror groups. "It could be said that Iraq emboldened Islamic groups in Egypt as well as Hamas in the PA," he said. "Democracy is not just about holding elections but it is about instituting a long list of democratic values and holding elections only at a later stage."