DAVOS, Switzerland, Jan. 24 (Xinhua) -- Israeli and Palestinian leaders reaffirmed here Thursday their commitments to the Annapolis peace process, with Israel urging the Palestinians to do more to rein in extremists, and the Palestinian side demanding easing of closure of the Gaza Strip.

    "Both sides are convinced that war is not the choice" Israeli President Shimon Peres told a session at the ongoing World Economic Forum (WEF) Annual Meeting. "We have got a partner of peace in the Palestinians."

    "The majority of the Palestinians are sincerely in favor of peace. We trust them full-heartedly. They are sincerely trying to achieve peace (with Israel) as soon as possible," Peres told the session under the theme of "Mideast: after Annapolis, after Paris" chaired by former British Prime Minister Tony Blair, the envoy of the Mideast Quartet.

    Peres said the Israeli-Palestinian peace process is now on two tracks: to solve the conflict, and negotiate the peace.

    Peres said the next 10 months are crucial for the peace talks, adding the hopes of a truce peace are "greater today."

    Israel and the Palestinians hope to finalize the peace talks before the U.S. presidential elections in November this year.

    The five-day Davos annual event, which opened Wednesday, has provided a good opportunity for Israeli and Palestinian leaders to talk face to face.

    Participants to Thursday's session also included Palestinian Authority (PA) Prime Minister Salam Fayyad, Israeli Foreign Minister Tzipi Livni and Israeli Defense Minister Ehud Barak.

    "We cannot afford a failure, we need success," said Livni.

    To achieve peace, both sides must make reconciliation and compromises, she said, adding that two states for two peoples is the only way out for the Israeli-Palestinian conflict.

    Meanwhile, she urged the PA to rein in extremists who are undermining the peace process, "we cannot afford an extremists' state."

    In his turn, Fayyad renewed the PA's commitments to the peace process, saying "we are determined to stay on the course."

    While stressing that the Palestinians took seriously Israel's security concerns, he also urged Israel to further ease the closure on the Gaza Strip, where the situation on the ground was "very dangerous." The closure by Israel had led to misery for the Palestinians, he said.

    In response to a sustained and intense barrage of rocket fire, Israel blocked Gaza and stopped all shipments except emergency supplies last week.

    Experts have warned that the Annapolis peace process could implode if something was not done quickly to address the Gazans' plight.

    Tens of thousands of Gazans have rushed into Egypt to search for food and supplies since Hamas militants blew 15 holes in a security fence separating the Gaza Strip and Egypt on Wednesday.

    Officials from the United Nations have called for an end to Israel's blockade of the Gaza Strip. The 15-member U.N. Security Council is to meet Thursday to discuss a draft statement urging an end to Israel's siege of the Gaza Strip and to rocket firing into the Jewish state from the strip.