The top US diplomat had hoped to use her visit to make "progress" over Israeli restrictions on access and movement, aimed in part at boosting Abbas in the face of the ruling Islamist movement Hamas, branded terrorists by the West.
Yet both the Israeli leadership and Rice's spokesman Sean McCormack listed only imprecise commitments on operating crossings in and out of the Gaza Strip, and considering the use of tax receipts to ease humanitarian concerns.
Prime Minister Ehud Olmert told Rice that Karni, the main export-import terminal between Gaza and Israel that has been closed for weeks, would reopen shortly but no precise date was given in a government statement.
Karni has been closed since August 15, affecting Gaza's vital supplies of food, medicines, and fuel in a territory where living standards have plummeted owing to aid freezes and Israel's bombing of the only power station in June.
Rafah has been closed almost continuously since Israel launched an offensive on Gaza in late June aiming to recover a soldier abducted by militants. It was open Thursday for a second day during the Muslim month of Ramadan.
"Israel has agreed that the Rafah crossing point ... will be open at regular intervals during the month. We are encouraged by this decision, the first step toward restoration of normal operations at the crossing," McCormack said.
"We also took favorable note of Israel's initial support" for a security plan prepared for the Karni crossing by a US security coordinator and the UN Agency for International Development.
Olmert's office said that the premier ruled out any question of releasing Palestinian prisoners until the captured Israeli soldier is freed. "Abu Mazen [Abbas] needs to be strengthened in order to create conditions for a resumption of negotiations with the Palestinians. But the question of releasing Gilad Shalit is the key to any advancement," defense minister Amir Peretz reiterated after meeting Rice Thursday.
Local media indicated that the government would be willing to release some money that it owes the Palestinian Authority in the form of tax receipts, but only to allow hospitals to operate and to buy medicines.
"The prime minister agreed to consider favorably the use of tax revenues for agreed humanitarian projects that will help the needs of the Palestinian population," McCormack said.
"[Olmert] said that Israel would present ideas on humanitarian assistance, such as aid to hospitals, medicines, etc," his office confirmed after Rice met with the premier over dinner Wednesday.
According to the World Bank, customs duties amounted to $65 million a month in 2005, or two-thirds of the Palestinian government's budget.
The withholding of the revenue, along with a Western freeze on direct aid since Hamas took office, has caused havoc in the Palestinian territories, prompting warnings from the United Nations of a humanitarian disaster.
On Wednesday, Rice met Abbas in Ramallah, where they united in declaring that any Palestinian government should respect the peace principles set out by the European Union, Russia, the United States, and the United Nations.
Hamas, which took office last March after winning a massive election victory over Abbas' moderate Fatah party, has stubbornly refused Western demands to recognize Israel, renounce violence, or abide by past peace agreements.
Abbas reiterated that stalled talks with Hamas on forming a unity government as a means could not go on forever and warned that "the Palestinian leadership will decide on the measures to take to get us out of this crisis."
As part of its efforts to boost Abbas, Washington is backing an international plan to boost the Palestinian presidential guard from 3,500 to 6,000 men, the senior State Department official said.
© 2006 Agence France-Presse