The Palestinian president and Israel's foreign minister have met the highest-level talks between the two sides since Hamas formed the Palestinian government in March.
Tzipi Livni said she told Mahmoud Abbas at the talks on Sunday that Israel, which has boycotted Hamas since it took office, wanted to help the Palestinian people.
Israel radio said Abbas and Livni would try to form a "bypass" channel to maintain communications without including Hamas in their talks.
The meeting, on the sidelines of the World Economic Forum, was attended by Abbas' chief negotiator, Saeb Erakat, and the Israeli deputy prime minister, Shimon Peres.
Erakat described the atmosphere in the talks as positive and said the two sides had agreed to meet again to lay the groundwork for a summit between Abbas and the Israeli prime minister, Ehud Olmert.
Ahead of the meeting, Abbas said that the "first and sole reference (in the peace process) is the road map", the peace plan drawn up by the US, Russia, the European Union and the United Nations.
"Our arms are stretched to (achieve) peace."
Livni did said the roadmap remained in force but did not elaborate.
Erakat said the Abbas team had reiterated requests for the Israeli government to release customs duties it traditionally collects on behalf of the Palestinian Authority but which have been frozen since February.
The 55 million US dollar transferred monthly to the Palestinian Authority up until a month after Hamas won the general elections was a major source of budget financing.
The Israeli cabinet partly responded to Abbas' plea by approving on Sunday the transfer of 11 million worth of medicine and health supplies to the Palestinians to help ease the deteriorating humanitarian conditions in the West Bank and Gaza Strip.
Palestinian hospitals have suffered from a lack of medicine since the aid freeze. Two people have died from lack of treatment and hundreds of dialysis patients are in danger, Israeli and Palestinian doctors from the group Physicians for Human Rights said last week.
The meeting in Sharm el-Sheikh comes against a backdrop of escalating tension in the Palestinian territories, with four Palestinians, including a local Islamic Jihad military commander, killed in an Israeli air raid on the Gaza Strip on Saturday.
Israel said it would open an investigation into the Gaza attack that left two women and a boy dead besides the Islamic Jihad fighter.
A Palestinian woman was also shot dead during a dawn raid by Israeli soldiers in the Balata refugee camp in the West Bank on Sunday.
Also on Sunday, Palestinians security officials said they had found a bomb outside the Gaza home of the residence of the overall chief of security, Rashid Abu Shbak.
The foiled attack came a day after the chief of intelligence, Tareq Abu Rajab, was seriously wounded along with seven others while one of his bodyguards was killed in a Gaza blast.
Abbas' Fatah and Hamas are caught in an increasingly violent power struggle focused on control of the security apparatus in Gaza.
Abbas vowed in Sharm El-Sheikh to revive internal talks with Hamas.
PHOTO CAPTION
Palestinians from the Fatah movement fall into formation during a rally in Gaza City. (AFP)