UNITED NATIONS - Israeli Defense Minister Ehud Barak on Thursday voiced his hope to find a new formula "in coming few weeks" to move forward the Middle East peace process, including the efforts to resume the direct peace talks between Palestinians and Israelis to address "direct issues" concerning the lengthy Mideast conflict.

"I believe we have to go over and beyond the hurdles of the second moratorium that somehow could not be delivered and move beyond it into the direct negotiations about the core issues in order to move forward," Barak said. "And we hope that a formula of this nature will be found in the coming few weeks in order to enable us to keep moving forward."

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Barak made the statement to reporters here after he met with UN Secretary-General Ban Ki-moon at the UN Headquarters in New York.

"I just ended a fruitful meeting with the secretary-general, we covered the Middle Eastern issue and the need to pursue the negotiation between us and the Palestinians in a way that contains both a sense of urgency and a sense of purpose," the minister said.

During the meeting, "I asked the secretary-general to use the influence that the UN enjoys with all players of the region to consider the situation, it is a strategic need of all peoples of the region," said Barak.

The formula described by Barak means that Israel seeks the resumption of direct talks with the Palestinians without a freeze on the settlement building in the occupied territory, observers here said.

The Barak-Ban meeting took place at a time when the secretary- general regrets that the Israeli government does not heed the appeal of the international community to extend a freeze on the Jewish settlement construction in the occupied territory.

Earlier this week, the United States gave up its efforts to persuade Israel to extend a moratorium on the settlement construction, which came as a foreign policy setback to the Obama administration.

Barak was in New York on his visit to the United States for talks with US officials aimed at salvaging the Middle East peace process.

The United Nations and the United States make up the Middle East Quartet, a diplomatic group in search of the two-State solution - a secure Israel to live in peace with an independent Palestinian State.

The Israeli settlement construction is illegal under the international law and derails the direct peace talk between the Palestinians and Israelis, relaunched in early September in Washington, the first of its kind in 19 months.

Also on Thursday, Palestinian President Mahmud Abbas said that the peace talks with Israelis will not be resumed until a halt is put to the settlement building.

"We will not accept negotiations as long as settlements continue," Abbas told reporters in Cairo after more than an hour of talks with Egyptian President Hosni Mubarak, reports said.