During a brief, unscheduled and warm encounter on Thursday afternoon in New York, Foreign Minister Tzipi Livni told President George W. Bush that he had helped advance Israeli-Palestinian peace hopes, and congratulated him for standing up to terrorism and extremism. Bush spoke briefly to both Livni and President Shimon Peres on the sidelines of an interfaith conference organized by the United Nations at the behest of Saudi Arabia. "They were not supposed to meet," Livni's spokesman told The Jerusalem Post. But as soon as Bush was done addressing the conference, the head of UN protocol approached Livni's staff and told them that the president wanted to speak with them. The president walked from the podium directly to them. "It was an extraordinary gesture," said Livni's spokesman, who said that the three talked in a side room. At the end, Bush took Livni aside for a one-on-one conversation and then left. During the meeting she told him, "In the aftermath of the elections here, it is important that the world knows that you have left behind you a [peace] process that continues to move forward and that you have moved the talks with the Palestinians in the right direction after years of terror. "No one can take this away from you," she added. "The whole world has to know this. You stood up against terror and extremism and helped return moderate Palestinians to the correct path with Israel. "For all this and much more, Israel should thank you," she said, according to text put out by the Foreign Ministry. Livni's spokesman would not disclose Bush's comments, saying only that they were "warm and personal." While in New York, Livni and Peres also met with Turkish Prime Minister Recep Tayyip Erdogan and Foreign Minister Ali Babacan. Ankara has been mediating indirect talks between Israel and Syria. Erdogan promised to continue to work for peace between Israel and its neighbors. He asked that Israel continue the Syria talks, even during the run-up to the February 10 elections. Peres said that while Israel was interested in peace with all its neighbors, "The Syrians have to decide if they want peace with Israel or with Iran. "Israel is not interested in having groups of armed Iranians on the Golan hills," Peres continued. "Syria has to decide which policy it wants to pursue - warm ties with Iran, which would be ties of terror, violence and religious extremism, or peace with Israel and the western world, that would usher in with it quiet and economic welfare." With respect to thwarting Iran's ambitions, Peres said that the coalition of moderate nations in the Middle East and the world had to be strengthened. As a moderate and democratic Muslim state, he said, Turkey was the antithesis of Iran. Erdogan also said he hoped the bilateral talks with the Palestinians would continue. Peres responded that "Israel and the Palestinian Authority have reached substantial agreements on the subjects of borders, security and even refugees." But it would take more time to come to an agreement, he said. Earlier in the day, Livni told an audience of Jewish leaders and donors in midtown Manhattan that the best way to achieve peace was to come to a final-status agreement that would guarantee two states. With the creation of a Palestinian state there would be no need for Palestinian refugees to return to Israel, she said. "If there is a problem of refugees who left Israel in 1948, this is not Israel's problem any more," she said. Livni also addressed the upcoming general election, citing her own career path through various ministries as she criticized a lack of stability in government. "A few weeks ago, I got a mandate to form a coalition and I could not," she said. "Israeli society pays the price - though in a way I am paying the price, because I am not prime minister today." According to Reuters, Livni also said that even after US President-elect Barack Obama takes office in January, Israel does not need any intensive intervention in the peace talks. "You don't need now to do anything dramatic about it. The situation is calm. We have these peace talks," she said. On Wednesday night, Livni held meetings with US Secretary of State Condoleezza Rice and United Nations Secretary-General Ban Ki-Moon. She also spoke Thursday with former US president Bill Clinton before heading back to Israel. Allison Hoffman contributed to this report.