U.S. President Barack Obama told Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas that "we must all take risks for peace" during a tripartite summit on Tuesday, U.S. envoy George Mitchell said.

Speaking at a press conference after the meeting, Mitchell also quoted Obama as telling the Israeli and Palestinian leaders that, "It's difficult to disentangle ourselves from history, but we must do so."

The special envoy to the Middle East further quoted Obama as saying: "Peace between Israel and the Palestinians is critical to Israel's security and is necessary for Palestinians to realize their aspirations."

Mitchell said that progress was made during the meeting, which was held at the Waldorf Astoria hotel. He added, however, that the parties had "much further to go."

"All sides must summon the will to move forward," he said. "Permanent status negotiations must begin, and begin soon. This was a message that the President conveyed to each of the leaders in private, as well."

Earlier Tuesday, Netanyahu said that he agreed with Abbas during the meeting that peace talks should be relaunched as soon as possible,.

"There was general agreement, including on the part of the Palestinians, that the peace process has to be resumed as soon as possible with no preconditions," Netanhayu told reporters in New York, after the summit with Obama and Abbas.

Obama launched the meeting by presiding over a handshake between the two leaders. The session was the highest level Israel-Palestinian meeting since Netanyahu took office in March.

"The importance of the meeting was actually its existence - in this case this common saying says a lot, because there was contact for half a year," said Netanyahu.

"This meeting brings back together people who have worked with each other for years, who have a real ability to change the face of the future."

Abbas, for his part, said that during the meeting he had repeated the Palestinian insistence that Israel halt construction in West Bank settlements and East Jerusalem.

In a statement he released after the summit, Abbas said: "In today's meetings we confirmed our positions and commitment to the road map and its implementation. We also demanded that the Israeli side fulfill its commitments on settlements, including on natural growth."

The Palestinian leader said that peace talks could only be resumed after they were based on the recognition of Israel's need to withdraw to its 1967 borders.

"This was reiterated in the talks with President Obama and in the trilateral talks," Abbas added. "We believe the American administration will review the positions of the two sides in the coming weeks to make it possible for us to renew peace talks based on our stated position."

Foreign Minister Avigdor Lieberman, who also participated in the session, said the staging of the summit was "important," but criticized the Palestinians for making demands on Israel regarding the West Bank.

"The Palestinian side said they have no preconditions, but the other side is demanding all sorts of steps in Judea and Samaria," said Lieberman, referring to the West Bank.

He added: "I think that from our point of view this government, with all of its complexity, has been ready from day one to sit down and immediately talk with all the sides and all the neighbors, without preconditions."

Defense Minister Ehud Barak also attended the meeting. He told Haaretz afterward that he did not interpret the president's comments as a "rebuke ."

Obama: Palestinians, Israel must do more for peace

At the start of the meeting, Obama urged the Israeli and Palestinian leaders to do more for peace.

"We cannot continue the same pattern of taking tentative steps forward and then stepping back," Obama told reporters as he sat down for the meeting. "Success depends on all sides acting with a sense of urgency."

The U.S. president said both sides must get formal peace negotiations back on track.

"Simply put, it is past time to talk about starting negotiations," Obama said. "It is time to move forward... Permanent status negotiations must begin and begin soon."

Obama said Mitchell would meet with Israeli and Palestinian negotiators next week, adding that he had asked his secretary of state, Hillary Clinton, to report back to him on the status of the talks in October.

The U.S. leader said everyone had worked tirelessly but still had not done enough.

To Palestinians, he said they must build on progress on halting terrorism and do more to stop incitement.

As for Israelis, he praised their moves to increase Palestinians' freedom of movement and their discussions about restraining settlement construction in the West Bank - both top Palestinian priorities.

"But they need to translate these discussions into real action," said Obama.

He said that since his administration took office in January there has been progress toward laying a foundation for the resumption of peace talks "but we still have much further to go." The U.S. president also called on Arab states to take concrete steps to aid the peace process.

The session came after Obama met separately with both men on the sidelines of the United Nations General Assembly session.

Click here for a timetable of the summit.

Netanyahu, Lieberman, Barak and National Security Council head Uzi Arad attended the first meeting, in which the U.S. secretary of state, Hillary Clinton, was also present.

In his meeting with Obama, Netanyahu said he wished to cooperate with the U.S. in its effort to resume peace talks, an Israeli official said. He spoke on condition of anonymity, in line with Israeli briefing regulations.

Obama met with Abbas after the meeting concluded.

The White House is making a last-minute diplomatic effort to come up with some significant statement signaling the revival of Israeli-Palestinian peace talks to conclude the summit, which will be held on the sidelines of the United Nations General Assembly.

Nonetheless, the White House said Monday that the administration had no "grand expectations" for Obama's meeting with the Israeli and Palestinian leaders.

Netanyahu, who landed in New York on Monday night, said recently that even if the peace talks are not resumed at the end of the summit meeting, they would start again after the holidays, in mid-October.

The Palestinians say the meeting will not constitute negotiations, since Abbas has refused to hold peace talks with Netanyahu until Israel freezes settlement construction.

Barak, who left for Washington on Sunday, met U.S. National Security Adviser General James Jones and the presidential adviser Dennis Ross. They discussed various formulas that would make the summit more than a mere "photo-op."