The Israeli and Palestinian leaders agreed at a U.S.-mediated meeting in Washington on Thursday to continue direct peace negotiations, with the next round scheduled for mid-September. U.S., Israeli, and Palestinian delegations held trilateral discussions in the U.S. Department of State on Thursday, followed by a smaller meeting of Israeli Prime Minister Benjamin Netanyahu, Palestinian President Mahmoud Abbas, U.S. Secretary of State Hillary Clinton and U.S. Special Envoy for Middle East Peace Process George Mitchell. The Israeli and Palestinian leaders then went into a separate meeting for a direct discussion, their first direct negotiations in 20 months. "They [Netanyahu and Abbas] agreed to meet again on September 14 and 15 in the region and roughly two weeks thereafter - every two weeks thereafter," Mitchell told a media briefing after the talks. "Of course, continued interactions at other levels between the parties and also yet others involving the United States will take place between those meetings," he added. Mitchell also said that the next meeting between the Israelis and Palestinians may be held in the Egyptian resort city of Sharm El Sheikh. The parties agreed that a logical next step would be to begin working on achieving a framework agreement for permanent status. "The purpose of a framework agreement will be to establish the fundamental compromises necessary to enable them to flesh out and complete a comprehensive treaty that will end the conflict and establish a lasting peace between Israel and the Palestinians," the U.S. official said. The sides also agreed that the negotiations on the core issues of the Middle East peace process can be completed within one year. Analysts have expressed doubts that the Israeli and Palestinian leaders can agree on the core issues, such as settlement construction, the status of East Jerusalem, Israel's demand for recognition as a Jewish state, the issue of Palestinian refugees and the final borders of a future Palestinian state. Before the talks, Abbas and Netanyahu expressed their willingness to search for a compromise. Netanyahu said that Israelis and Palestinians now have "a real opportunity to put an end to the conflict." He added that Israel was "prepared to walk this road and to go a long way in a short time to achieve a genuine peace that will bring our people security prosperity - and good neighbors" "A true peace, a lasting peace will be achieved only with mutual and painful concessions from both sides," the Israeli premier said at the official launch of the talks. Abbas, in his turn, said that the two-state solution was key to peace in the region and reiterated calls on Israel to end all settlement activities and completely lift the embargo over the Gaza Strip U.S. Secretary of State Hillary Clinton said the U.S. would continue its support for the Middle East peace process. "We cannot and we will not impose a solution," Clinton told Abbas and Netanyahu. "Only you can make the decisions necessary to reach an agreement and secure a peaceful future for the Israeli and Palestinian people."