Israeli and Palestinian negotiators began addressing the most difficult issues of their decades-old conflict Monday, keeping a promise to President Bush but putting Israel's coalition government under strain.

Israeli Foreign Minister Tzipi Livni and former Palestinian Authority Prime Minister Ahmed Korei emerged from a two-hour session at a Jerusalem hotel with little to say about what they had discussed. Israeli officials said the two lead negotiators planned to meet at least once a week.

The two sides agreed on Nov. 27 at a U.S.-sponsored international conference in Annapolis, Md., to resume full-scale peace talks after a seven-year hiatus. The aim is to agree by the end of Bush's presidency on the terms for creation of an independent Palestinian state.

But a dispute over new Jewish housing construction on land claimed by the Palestinians had stalled the talks, and it took Bush's visit to Israel and the West Bank last week to get them going.

"It was an exploratory session, and we exchanged our views on how to approach the core issues," Korei told reporters after Monday's meeting. "The talks were positive, but the path ahead is difficult."

Those issues, now on the table for the first time since a U.S.-led peace effort in the final months of the Clinton administration, include the borders of a Palestinian state, the fate of Palestinian refugees who fled what is now Israel, and conflicting claims to Jerusalem.

Livni told parliament Monday that she was prepared to make significant territorial concessions to achieve peace, but she emphasized that no land would change hands until the Palestinian Authority showed it could quell militant activity and ensure Israel's security.

The talks would be conducted quietly, away from the "glare of the cameras," she said, to avoid the grandstanding and raised expectations that "led to disappointment and violence" after the Clinton effort collapsed.

"Faced with a choice between headlines and daily drama as opposed to results, I choose results," she said.

Israeli Prime Minister Ehud Olmert also wants to limit any grounds for dissension among his supporters as the talks progress. Avigdor Lieberman is threatening to pull his right-wing Israel Our Home party from the governing coalition as early as this week to protest the mere fact that the most sensitive issues are being discussed.

Lieberman's decision could sway the ultra-Orthodox Shas Party, which opposes territorial concessions to the Palestinians. Without those two parties, Olmert's coalition, anchored by his centrist Kadima party and the left-leaning Labor Party, would lose its parliamentary majority and be forced to scramble for new partners to stay in power.

Olmert's task of sustaining support for peace talks is complicated by his vulnerability on another issue: Israel's war against Hezbollah guerrillas in Lebanon in 2006, widely seen as ending in a stalemate. An official inquiry panel's second report on his government's conduct of that war is due Jan. 30 and is likely to prompt calls for Olmert's resignation.

Bush and coalition party leaders attended a working dinner Thursday at Olmert's residence, during which the U.S. president urged them to rally behind the prime minister and the peace effort. According to participants' accounts in the Israeli newspaper Haaretz of the closed-door dinner, Bush then observed: "Israeli politics is like karate. You never know when the next chop will come."

Palestinian Authority President Mahmoud Abbas is also weakened by his secular Fatah-led administration's loss of the Gaza Strip in June to the militant Islamic movement Hamas, which calls for Israel's destruction, and his limited ability to control militant activity in his own West Bank stronghold.

In Gaza, Hamas spokesman Sami abu Zuhri told the Reuters news agency that the peace talks were aimed at providing "a cover for the occupation crimes against our people" by Israel and were doomed to fail.