Top Israeli and Palestinian negotiators began talks on core issues on Monday, as Prime Minister Ehud Olmert of Israel sought to lower expectations of reaching a final peace agreement within a year.

“I’m not sure we can reach an agreement, and I’m not sure we can reach its implementation,” Mr. Olmert told Parliament’s foreign affairs and defense committee on Monday, an official who had attended the meeting said.

But Mr. Olmert said he would be “committing a sin to my duty” if he did not try, and called what he described as the right-wing opposition’s position of wanting to maintain the status quo “dangerous, adventurous and irresponsible.”

Tzipi Livni, Israel’s foreign minister, and Ahmed Qurei, the former Palestinian prime minister, met in a hotel here for two hours, without aides, charged by their leaders with discussing the contentious issues that must be resolved for any final status deal.

Being broached for the first time in seven years, the issues include borders, the fate of the Palestinian refugees of the 1948 war and their descendants, and the status of Jerusalem, the eastern part of which the Palestinians demand as the capital of any state.

President Bush said last Thursday in the West Bank that he believed a treaty would be signed by the time he left office in January 2009.

Back in Jerusalem the same day, Mr. Bush expressed his views on some of the major issues, including the need for “mutually agreed adjustments to the armistice lines of 1949 to reflect current realities,” a reference to populous Jewish settlement blocs in the West Bank that Israel intends to keep; and a solution to the refugee issue based on compensation and movement to a new Palestinian state, rather than a return to the refugees’ former homes in what is now Israel.

On Monday, Ms. Livni said the negotiations would be “conducted quietly,” away from cameras, to prevent the talks from becoming overly political, according to a statement from her office. “Faced with a choice between headlines and daily drama as opposed to results, I choose results,” Ms. Livni said.

“We need to make 2008 the year of peace and a treaty,” Saeb Erekat, a senior Palestinian negotiator, said in an interview. “I really believe it’s doable.”

The sides “are not beginning from scratch,” he said. “We have had many negotiations in the past, and we don’t need to reinvent the wheel.”

The Israelis were satisfied with Mr. Bush’s statement last week. “We view it positively,” said Arye Mekel, a spokesman for Ms. Livni, adding that “it coincides with understandings we’ve reached with the United States.”

The Palestinian side was less enthusiastic. “Some of the things he said we agree with, and some we disagree with,” Mr. Erekat said, adding, “At the end of the day, what we need are Israeli-Palestinian agreements” rather than “decisions” from Mr. Bush.

Mr. Olmert’s remarks on Monday might have been intended partly for internal consumption, with two of his more hawkish coalition partners, the nationalist Yisrael Beiteinu Party and the religious Shas Party, having threatened to leave the government if the talks become serious.

Mr. Olmert has tried to assuage the ministers who lead those parties, inviting them to a dinner with Mr. Bush Thursday.

“The prime minister wants to move ahead on the peace process and understands that the best way to do that is to keep the coalition stable and maintain a solid political base,” Mark Regev, a spokesman for Mr. Olmert, said.

But Avigdor Lieberman, who leads Yisrael Beiteinu, was further angered by Mr. Olmert, who said in an internal meeting on Sunday that Israel’s failure to remove illegal outposts in the West Bank was “a disgrace,” said an official who was at the meeting and did not want to be identified because he was not authorized to speak about it. Israel has long committed itself to removing about 26 outposts set up after March 1, 2001, and Mr. Bush expressed his annoyance here about the delay in their removal, saying they had “to go.”

Critics of Mr. Olmert, who has been prime minister for two years, expressed surprise that he would blame anyone but himself.

Ophir Pines-Paz, a Labor legislator, said: “The disgrace is the helplessness and idleness displayed by Olmert on the issue of outpost evacuation. Olmert has turned the promises made by Israel into a joke.”

Mr. Olmert did not say who was to blame for not removing the outposts, but some interpreted his criticism as being aimed at the defense minister, whose purview includes the settlements.

In what seemed to be a rebuttal, the daily newspaper Haaretz on Monday cited “sources close to” the defense minister, Ehud Barak, saying that he had agreed with leaders of the settlement movement on the peaceful evacuation of 18 outposts, but that Mr. Olmert had repeatedly opted to postpone the deal.

Yishai Hollender, a spokesman for the Yesha Council, which represents Jewish settlers, said in an interview that there had been dialogue between the defense minister’s representatives and the settlers, but no agreement. He said the prime minister’s office had “torpedoed attempts” to reach an agreement “time after time,” and had been unwilling to accept the settlers’ terms.

Mr. Regev said that he was “not aware” of tension between Mr. Olmert and Mr. Barak, and that they were “on the same page.”