Amid growing internal tension in the Palestinian territories between Hamas and Fatah, Foreign Minister Tzipi Livni and Vice Premier Shimon Peres will meet with Palestinian Authority Chairman Mahmoud Abbas at an economic summit in Egypt on Sunday, while the government pushes forward with a humanitarian aid proposal to transfer needed medicine to the Palestinians, officials said Friday. The meeting, which will be held on the sidelines of the World Economic Forum taking place in the Egyptian resort of Sharm el-Sheikh, would be the first high-level contact between Israelis and Palestinians since Hamas won a stunning upset victory in January's Palestinian legislative elections. Chief Palestinian negotiator Saeb Erekat is also due to take part in the scheduled half-hour meeting. The encounter, which comes on the very day Prime Minister Ehud Olmert leaves Israel for his first official trip to Washington since taking office earlier this month, is bound to be welcomed by the American administration, which has been encouraging such contacts in the hopes of bypassing Hamas. Three of the prime minister's top aides, who were in Washington this week to lay the groundwork for his meetings with top American officials, are believed to have come under pressure there to impress on Olmert to try to negotiate a final peace deal with Abbas, rather than unilaterally draw Israel's final borders with the West Bank, which has been met with strong international opposition, especially in Europe. The premier has repeatedly said that he favors direct negotiations with the Palestinians, but would act unilaterally to redraw Israel's borders in the next couple years if it becomes clear in the next six months that such talks are impossible. Olmert himself said Wednesday in a meeting with the French Foreign Minister, Philippe Douste-Blazy, that he is willing to meet with Abbas, but added that he doubts that negotiations with a Hamas-led Palestinian government will get anywhere. The prime minister is expected to meet the weakened Palestinian leader in the coming weeks, after returning from Washington and meeting with both Arab and European leaders. In the meantime, amid an increasingly bleak economic situation in the cash-strapped Palestinian territories, the prime minister is preparing to bring forward a proposal to the Cabinet meeting on Sunday whereby Israel would buy and transfer medicine to Palestinian hospitals with the tens of millions of dollars of frozen tax money it collects for the Palestinian Government, Olmert spokesman Assi Shariv said Thursday. The plan, which is still being worked on, is expected to be immediately approved, and could be put into action as early as next week. Israel would even put up its own money if necessary to provide essential supplies to the hospitals "as soon as possible," Olmert said in an interview with The New York Times. "We wouldn't allow one baby to suffer one night because of a lack of dialysis. We care," he said. "We want to save their lives." After the shock Hamas victory, most Western nations, which previously poured about $1 billion a year in aid to the Palestinian Authority, decided to only fund humanitarian projects without going through the Hamas-led Palestinian government.