The latest: Palestinian and Israeli negotiators sat down Monday to address their toughest disputes, honoring promises made to President Bush during his visit last week.

Israeli Foreign Minister Tzipi Livni, Israel's lead negotiator, and chief Palestinian negotiator Ahmed Qureia met for two hours at a Jerusalem hotel, and Israeli officials said meetings were expected to continue on a more or less weekly basis.

Core issues: "They started talking about the core issues," Israeli Foreign Ministry spokesman Arye Mekel said, referring to questions such as the borders of a Palestinian state, the status of Jerusalem and the future of Palestinian refugees. Qureia called it an "exploratory session."

Threat to coalition: The talks were undermined by a hawkish Israeli lawmaker's threat to bolt Prime Minister Ehud Olmert's coalition government as he tries to clinch a peace deal. Avigdor Lieberman, head of the Israel Our Home Party, was to meet with Olmert today and decide whether to remain in the government, Lieberman's spokeswoman said.

Olmert's coalition would still command a majority -- 67 of parliament's 120 seats -- if Israel Our Home's 11 lawmakers were to leave.

Another defection possible: But the ultra-Orthodox Shas Party, which has 12 seats, has also threatened to leave the coalition. Shas rejects any territorial compromise over Jerusalem, while the Palestinians claim the eastern section as the capital of the state they want to create. A Shas defection would leave Olmert scrambling to rebuild a parliamentary majority.