Rice, who urged Israeli and Palestinian leaders to capitalize on peace prospects raised by Israel's Gaza pullout, was unable to announce a compromise over greater freedom of movement for Palestinians to and from the coastal strip.
But seeing a chance for rare progress in Middle East diplomacy, Rice planned to fly to Jordan as scheduled to pay her respects after last week's hotel bombings and then return to Israel on Monday night instead of heading for
South Korea.
Gaza's border crossing to Egypt, its main outlet to the outside world, has been closed since Israel withdrew in September. Reopening it is seen as crucial to boosting the territory's crippled economy and creating momentum for long-stalled peacemaking.
"We are still working the issue on both sides," Rice's spokesman, Sean McCormack, said. Washington has said resolving the Israeli-Palestinian conflict is a foreign policy priority, though critics have accused it of failing to engage fully.
In separate talks earlier on Monday, Rice pressed the Palestinians to "fight terror" and urged Israel to freeze
West Bank settlement expansion, obligations under a U.S.-sponsored peace "road map" stymied by violence and non-compliance.
U.S. officials have voiced frustration at both sides' failure to capitalize on what Washington has seen as an opening for renewed peace moves following Israel's first removal of settlements from land Palestinians want for a state.
Sporadic fighting has put a damper on diplomacy. In the latest flare-up, Israeli troops shot dead a Hamas commander in the occupied West Bank and killed another gunman preparing an attack on the Gaza frontier. Militants vowed revenge.
Rice's visit, her fourth to the region this year, was also overshadowed by an Israeli political upheaval threatening to bring down Prime Minister
Ariel Sharon's government and force early elections, a climate likely to keep peace moves on hold.
BRINGS SIDES CLOSER
Despite that, Rice brought the sides closer to a deal on reopening Gaza's Rafah border crossing to Egypt as well as creating a land passage between Gaza and the West Bank.
"It is very important for ordinary Palestinians ... that there be freedom of movement established between Gaza and the West Bank," Rice told a news conference with Palestinian President Mahmoud Abbas in Ramallah. "There is agreement in sight."
Israel, which has kept control of Gaza's borders and air space since the withdrawal, has been under U.S. pressure to reopen the Rafah terminal to Palestinian trade and travel to help ease hardships for Gaza's mostly impoverished population.
But differences appeared to center on Israeli monitoring of the Rafah terminal, where both sides have agreed to
European Union observers.
Citing security concerns, Israel has pushed for a video link through which it could view Palestinians crossing the frontier. Palestinians oppose this.
Abbas said an agreement was imminent but final details still had to be worked out. A reopened border would boost his standing with Palestinians before a January parliamentary election in which the militant group Hamas is posing a strong challenge.
Rice had been expected to press Abbas to rein in militants from Hamas, which is dedicated to Israel's destruction. "We talked about the need to condemn and fight terror," she told reporters.
Sharon reiterated on Sunday his stand that peace talks could be held only after Palestinians met their road map obligation to disarm militants.
Rice also said Washington wanted Israel to fulfil its road map requirement to stop expanding Jewish settlements in the West Bank. Sharon has moved to strengthen Israel's hold on major settlement blocs he says the Jewish state will never relinquish.
"We've made it clear that there should be no activity that prejudges a final status agreement," Rice told reporters.
(Additional reporting by Ori Lewis in Jerusalem, Wafa Amr in Ramallah, Atef Sa'ad in Nablus and Nidal al-Mughrabi in Gaza)
