The U.S. and Israel agreed ahead of a three-way meeting with the Palestinians not to work with any new Palestinian government that does not renounce violence, recognize Israel and accept existing peace agreements, Prime Minister Ehud Olmert said Sunday.

The so-called Quartet of Mideast negotiators — the U.S., European Union, U.N. and Russia — has set these demands as a condition for lifting crippling international sanctions against the Palestinians. The platform of a new Palestinian power-sharing agreement reached this month speaks only of "respect" for existing peace deals.

In the West Bank town of Ramallah, Palestinian President Mahmoud Abbas on Sunday tried to persuade visiting Secretary of State Condoleezza Rice to give the Hamas-Fatah coalition a chance, his aides said on condition of anonymity because they were not authorized to discuss the matter with the media.

During the meeting, Rice said the U.S. position is unchanged, a senior American official said, speaking on condition of anonymity because the talks were private. He said the U.S. would withhold judgment until the Palestinian government is formed. "We will reach our own conclusions," he said.

• Visit FOXNews.com's Mideast Center for more in-depth coverage.

The Palestinian officials said Abbas, in turn, told Rice that his deal with Hamas was the best he could get, suggesting change in the government's program was unlikely. He also emphasized that he, not the government, would handle negotiations with Israel, and Rice assured him the U.S. would continue dealing with him, his aides said.

Later Monday, Rice was to meet with Olmert, ahead of Monday's trilateral summit. The summit on Monday was initially billed as an attempt to revive long-stalled peace talks, but has been eclipsed by friction over the power-sharing deal.

Olmert said at the start of the weekly Cabinet meeting Sunday that he and President Bush had spoken by phone about the deal and agreed the Palestinians had to go further.

"A Palestinian government that won't accept the Quartet conditions won't receive recognition and cooperation," Olmert said. "The American and Israeli positions are totally identical on this issue."

In the northern Gaza town of Beit Hanoun, Palestinian Prime Minister Ismail Haniyeh of Hamas accused the U.S. and Israel of trying to sabotage the unity deal, which has helped halt months of deadly fighting.

"The American and Israeli interference today aim to destroy the basic principles and the basis of the Palestinian cause ... and to divert our cause," he said.

Abbas had tried during months of coalition talks to press Hamas to agree to abide by existing peace accords — something that would imply recognition of Israel — but yielded after multiple rounds of deadly Palestinian infighting.

Complete coverage is available in FOXNews.com's Mideast Center.