Olmert said: "I am going to make every possible effort to move forward to see how things can be worked jointly, in order to provide Palestinians a real, genuine chance for a state of their own."
He had said earlier this week he was ready to renew regular contacts with the Palestinian president in order "to resolve the outstanding daily issues and move forward to finding ways to solve grander issues."
"Hamas must decide what their objective is - is it power, is it Israel's destruction, or is it peace for the Palestinian people?
Chris, Stockholm, Sweden
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Israel and the United States want to isolate Hamas financially, diplomatically and militarily in the Gaza Strip, while throwing their support behind Abbas' new emergency government comprised of Fatah loyalists.
The US and EU pledged on Monday to lift an economic and diplomatic embargo on the Palestinian government of Fatah loyalists Abbas formed in the West Bank.
The embargo was imposed on the Palestinian Authority in March 2006 following Hamas’ election victory and refusal to recosgnise Israel.
Bush and Olmert met in the aftermath of a week of fighting that left Abbas, a Western-backed moderate, in control of the West Bank and Hamas in control of the separate Gaza Strip on the coast.
The US and EU have been moving quickly to shore up support for Abbas.
Condoleezza Rice, the US secretary of state, announced on Monday announced an end to an economic and political embargo on the Palestinians.
Israel has seemed likely to free up millions in tax revenue it collects on behalf of the Palestinians, assuming it could ensure that the money flowed only to Abbas' operation in the West Bank.
"Like you, I want to strengthen the moderates," Olmert said.
Israel plans to bar Palestinian tax funds transferred to Abbas from reaching Gaza to run Hamas-led agencies and pay workers, two senior Israeli officials said.
Riyad al-Malki, the Palestinian information minister, said the emergency government knew of no Israeli conditions on the tax funds which Israel collects on the Palestinian Authority's behalf. "We will not accept any conditions," he said.
Majdi al-Khalidi, an adviser in Abbas' office, told Western diplomats the emergency government could remain for a period of two months and then become a caretaker administration that could try to lay the ground for new elections.
A senior Western diplomat said Abbas' office made clear it does not want the international community to have "any contact or provide any legitimacy to Hamas in Gaza" except to facilitate the delivery of humanitarian assistance.
The flow of water and power would not be affected but Gaza would face severe restrictions, including a freeze on exports while Hamas is in power, the diplomat said.
Israeli officials say up to $400 million in Palestinian tax revenues will be transferred to Abbas's emergency government in stages, short of the $700 million sought by Abbas. Israel says the rest of the money has been frozen by court order.
It is unclear if the EU will go along with Israeli efforts to isolate Gaza, whose 1.5 million residents are dependent on aid.