Story Highlights• NEW: Israeli PM says money can't go to government
• NEW: Unfrozen funds should go to hospitals, spokeswoman says
• NEW: Leaders discuss easing border crossings
• Leaders agree to set up committee on prisoner exchange
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JERUSALEM (CNN) -- Israel is willing to transfer $100 million to Palestinians for humanitarian needs, Israeli Prime Minister Ehud Olmert's spokeswoman said Saturday night after Olmert met with Palestinian President Mahmoud Abbas.
However, Miri Eisin told CNN the money will be released only if a way is found to transfer the now-frozen funds directly to Palestinians -- without going through the Hamas-led government.
"The international community was the one that defined clearly that the money could not go through that government. We want it to arrive at hospitals -- for medical supplies, for the different things that are needed to alleviate the Palestinian suffering," Eisin said. (Watch Eisin discuss what happened in the meeting )
The $100 million is only part of the revenue from tax rebates and other sources that Israel froze after the Islamic militant group Hamas came to power in March. The European Union and the United States have designated Hamas a terrorist group for its goal to destroy Israel.
In a statement released by Olmert's office early Sunday, the summit was described as a step in reviving the peace process between Israel and the Palestinians, which broke down in September 2000.
"During the meeting, which was conducted in a good and friendly atmosphere, the two men expressed their willingness to cooperate -- as genuine partners -- in an effort to advance the peace process between Israel and the PA (Palestinian Authority)," the statement read.
Olmert agreed during the talks to open some of the roadblocks in the West Bank that prevent Palestinians from entering Israel for jobs and other reasons, Eisin said.
The men discussed the cease-fire in Gaza that went into effect about a month ago and the possibility of expanding that to the West Bank. Since the Gaza cease-fire, Palestinian militants in Gaza have launched more than 50 rockets toward Israel, she said.
The statement from Olmert's office said he and Abbas agreed "to make a genuine effort to upgrade the crossings between the Gaza Strip and Israel in order to facilitate better passage for goods and people."
The two sides will improve efficiency of security checks at crossings to reach a target of 400 trucks a day between Gaza and Israel, and to promote the possibilities of trade between Gaza, the West Bank and Israel, the statement said.
Saeb Erekat, a legislator and top aide to Abbas, told a news conference in Ramallah that the Palestinians agreed to form a joint committee with the Israelis to work out the details of a possible prisoner exchange.
One especially sought-after Israeli prisoner is Israeli soldier Gilad Shalit, who was captured by militants in June.
Abbas made clear that he supports a two-state solution to the violence and wants more dialog with Israel, Eisin said. Israel supports that view, she added.
"The essence of tonight's meeting ... was about dialog and about going forward on a road to try and find at the end a resolution between the Palestinians and Israel," Eisin said.
The men met for about two hours at Olmert's Jerusalem residence.
Factional tension continues
The meeting comes amid continuing tensions in the Palestinian territories between Abbas' Fatah party and the Hamas movement, which controls the government.
Last week, Abbas called for early legislative elections, a move strongly opposed by Hamas, and the balloting was to be discussed at the meeting.
It was the first time that Olmert and Abbas have met in their respective positions. They were supposed to meet in June, but that was canceled because of the Shalit capture.
Israeli and Palestinian sources said there have been many meetings over the last several months between the offices of both leaders to establish a dialogue and lay the groundwork for a meeting. The men vowed to have frequent meetings to help resolve issues.
Israeli officials regard Abbas as a potential partner for peace with the Palestinians, but view him as hampered by the Hamas-led government.
Olmert recently paid a visit to Jordan's King Abdullah II, discussing a wide range of issues including how to improve deteriorating conditions in the Palestinian territories.
CNN's Elise Labott contributed to this report.
Palestinian Authority President Mahmoud Abbas, left, arrives Saturday at the Jerusalem residence of Israeli Prime Minister Ehud Olmert, right.
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