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.
"It is a terrorist government. On the other hand we want to help the Palestinian people and not to punish them ... This was part of the discussion," she told reporters after the 45-minute talk at the Egyptian resort of Sharm el-Sheikh.
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's chief negotiator, Saeb Erikat, and Shimon Peres, the Israeli deputy prime minister.
Erikat 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 Ehud Olmert, the Israeli prime minister.
But Olmert said on Sunday that Abbas was powerless to speak on behalf of his people, raising doubts over the prospects for any Israeli-Palestinian peace efforts.
"He is powerless. He is helpless. He's unable to even stop the minimal terror activities amongst the Palestinians," Olmert told CNN.
"[Mahmoud Abbas] is powerless. He is helpless. He's unable to even stop the minimal terror activities amongst the Palestinians. So how can he represent that government in the most crucial, complex and sensitive negotiations?"
Israeli prime minister
"So how can he represent that government in the most crucial, complex and sensitive negotiations, about which there are so many divisions within the Palestinian community?"
Before the meeting with Livni, Abbas had 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.
Livni said the road map remained in force, but did not elaborate.
Erikat said the Abbas team had reiterated requests for the Israeli government to release customs duties it collects on behalf of the Palestinian Authority but which have been frozen since February.
Livni (R) is Olmert's number two
in the new Israeli cabinet
The $55 million transferred monthly to the Palestinian Authority up until a month after Hamas won the elections was a big source of budget financing.
The Israeli cabinet partly responded to Abbas's 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.
Olmert said before the cabinet meeting: "We have no intention of helping the Palestinian government. We will not transfer one cent to any Palestinian official but ... we will transfer above and beyond what is necessary for humanitarian needs."
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 growing 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.
A Palestinian fighter was killed
in Gaza by Israelis on Saturday
Islamic Jihad fired five rockets at the southern Israeli town of Sderot, one of which hit an empty classroom.
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's 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.
"Civil war is the red line that nobody dares cross, no matter which side they are on ... Civil war is forbidden," he said.
Olmert flew out of Israel to Washington on Sunday for his first meeting with George Bush, the US president, since winning the general election in March.