The Palestinian Authority is expecting US Secretary of State Condoleezza Rice to provide it with a "face-saving device" that will allow it to return to negotiations with Israel, according to assessments in Jerusalem on the eve of Rice's visit. Rice is scheduled to arrive at noon Tuesday, after spending some five hours in Egypt. The prevalent feeling in Jerusalem is that despite the recent flare-up in Gaza, her discussions in Cairo will focus on securing an agreement between Egypt, the Palestinian Authority and Hamas regarding the border situation. Such an agreement, according to this assessment, would be the incentive to get the Palestinian Authority back to the negotiating table. PA President Mahmoud Abbas suspended talks with Israel on Sunday because of the fighting in the Gaza Strip. According to official assessments in Jerusalem, the PA does not want to call off the negotiations, if for no other reason than continuing talks is the only card it holds. "Without the negotiations, the Palestinian Authority doesn't have anything," one senior government official said. "The fact is that the international community pledged billions of dollars to them in Paris because of [the PA's] commitment to Annapolis and negotiations. If they stop the negotiations, they will lose that international support, and without that, they have nothing - they don't have Gaza, and they barely have control of the West Bank." According to this official, the IDF's surprise pullout from Gaza on Monday was timed to coincide with Rice's visit, in order to give her an opportunity to try to work out some kind of border agreement. When Rice's visit was first planned several weeks ago, it was expected to focus on two main issues: coming up with some kind of security regimen on the Gaza-Egypt border following the breach there in January, and pushing the diplomatic process with the Palestinians forward. The intensified fighting in Gaza, however, threatened to change the focus of her talks completely. "The fact that we stopped the military action allows her to go back to the original aims, to address an agreement on Rafah," the official said. Foreign Minister Tzipi Livni, at a meeting with the foreign diplomatic corps in Jerusalem Monday, stressed that the IDF leaving Gaza Monday morning did not mean that Israel's actions there were over. Indeed, Livni - who also met Monday with visiting EU foreign policy chief Javier Solana - indicated that the military operation's goals were not only to stop the rocket fire, but - even more importantly - to halt Hamas's arms buildup and weaken its hold on Gaza. Livni said that any decision the government took on how to deal with Gaza would be based on the following objectives: providing security for Israeli citizens, harming Hamas militarily, and hurting the organization diplomatically. "Those who control Gaza are responsible for what happens there. We will not play by their rules, we will change the game whereby they decide when to attack, when to stop and for how long... We will decide when to stop our actions. That the soldiers left Gaza today... is not the end of our activity against terror in Gaza, which will continue," she said. The security cabinet is expected to meet Wednesday and discuss the army's overall objectives in the Strip. "We need to attack [Hamas's] infrastructure, the places where weapons are made and the terrorists themselves. But that's not enough. Anyone who wants to solve the terrorist problem from Gaza needs to prevent Hamas's buildup," Livni said. Livni alluded to the fact that the results of Israel's actions in Gaza would have wider ramifications, echoing the position of Maj.-Gen. Amos Yadlin, head of military intelligence, who said at Sunday's cabinet meeting that Iran, Syria and Hizbullah were carefully watching the situation in Gaza. "No one has an interest in Hamas's success expect for Iran, Syria and Hizbullah," Livni said. "Its success is not a matter of reality, but also one of perception." Livni added that the regional players could not accept a spin of a Hamas victory - not Abbas, not Israel, and not the moderate Arab states. In Washington, meanwhile, a State Department official said the US "wants to see negotiations resume, and we believe it's important that the parties continue to try to work through the Annapolis process to achieve the results that they've committed themselves to." The official said Rice would be making it clear that Hamas must stop the rocket attacks, which hurt the Palestinian people as well as Israelis. Earlier Monday, White House spokesman Gordon Johndroe said the US would use the visit to stress the decision that is now facing the Palestinians. "We have a clear message: The Palestinian people have a choice to make. It's a choice between terrorism, or a choice between a political solution that leads to a Palestinian state living side by side in peace and security with Israel," he said. He also had harsh words for Hamas, whom he blamed for the fighting. "The number one thing that has to happen is that Hamas has got to stop targeting Israeli citizens with rockets," he said. When asked if Israel's response to the Gaza rocket fire had been disproportionate in the eyes of the US, Johndroe responded, "We obviously don't want any innocent civilians to lose their lives, but I think that started with these rockets that have been fired from Gaza into Israel, recently killing and injuring Israeli citizens in some of their bigger cities." He described the situation as being "escalated" by Hamas to "firing larger rockets longer-range and killing people. That's got to stop," he aid. Livni, meanwhile, said before her meeting with Solana that "these were not easy days for Israeli citizens. Israel is in the midst of a struggle against terrorism and will continue in this war against terror." The foreign minister said that Israel expected the international community to support its war against terror and "show determination" in delegitimizing terrorist organizations, first and foremost - Hamas. Livni's comments came even as Italy's foreign minister called on Israel to negotiate with Hamas to bring about a cease-fire. Hilary Leila Krieger contributed to this report.