JERUSALEM — Israeli and Palestinian negotiators took on the most contentious issues in their bitter conflict Monday, under a U.S.-backed effort to reach a final peace deal by the end of the year.

The talks' new direction threatened to draw Israeli Prime Minister Ehud Olmert into a coalition crisis, because two key partners have threatened to bolt his government should negotiators broach the charged questions of shared sovereignty over Jerusalem, final borders and Palestinian refugees.

Israeli Foreign Minister Tzipi Livni, Israel's lead negotiator, and chief Palestinian negotiator Ahmed Qureia met Monday for two hours at a Jerusalem hotel.

"They started talking about the core issues," Israeli Foreign Ministry spokesman Arye Mekel confirmed. The two plan to meet about once weekly, Israeli officials said, but had no further details. There was no immediate comment from the Palestinians.

At a U.S.-sponsored conference in late November, the two sides relaunched negotiations after seven years of violence, hoping to reach an agreement before President Bush leaves office a year from now. But talks stalled immediately over Israeli construction in disputed territory and Palestinian militant activity.

Last week, before Bush arrived in the region to try to propel negotiations forward, Palestinian President Mahmoud Abbas and Olmert instructed negotiators to start discussing the thorny issues.

The new focus could, however, deepen internal divisions in Israel's government.

Avigdor Lieberman, the hawkish lawmaker who is head of the Yisrael Beiteinu Party, has threatened to pull out of the coalition if the government begins discussing the questions at the heart of the Israeli-Palestinian conflict. The ultra-Orthodox Shas party has made a similar threat and if both leave, Olmert will lose his parliamentary majority.

Lieberman also opposes Israel's commitment to the U.S. to evacuate some two dozen unauthorized settlement outposts — encampments settlers erected across the West Bank to break up territory the Palestinians claim for a future state. On Sunday, days after Bush said in Jerusalem that the outposts "ought to go," Olmert told political allies it was a "disgrace" they remained standing four years after Israel promised to pull them down.

Israel is trying to reach a peace deal with Abbas while fighting Islamic militants in Hamas-run Gaza who fire rockets and mortars at southern Israel almost daily.

Even before Livni and Qureia sat down for their talks, Hamas spokesman Sami Abu Zuhri demanded that Abbas "stop giving away Palestinian blood and rights for free."

"This is a failed meeting that is going to provide a cover for the occupation crimes against our people," Abu Zuhri told reporters.

Hamas wrested control of Gaza from Abbas-allied forces in June. The militant Muslim group is isolated internationally and is not a party to the negotiations. Olmert has said repeatedly that Israel would not implement any peace agreement before Gaza militants were subdued.

In his remarks before the parliamentary panel, Olmert reiterated his doubts about Abbas' ability to reassert control over Gaza, another meeting participant said on condition of anonymity because the session was closed.

"I'm not sure the man leading the Palestinian Authority will have the power to bring about the implementation of the agreement," Olmert was quoted as saying.

Olmert also suggested to the panel that he wasn't interested in a broad military operation against Gaza militants. "If we need to do more, we will, but there's no need to become overzealous," he was quoted as telling lawmakers.

Defense Minister Ehud Barak repeatedly has said a large-scale operation was in the offing. Previous broad strikes have failed to halt the rocket fire while causing heavy Palestinian civilian casualties and damage.