Fierce opposition to the roadmap remains among some Israelis
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The Israeli and Palestinian leaders have urged each other to take practical steps to peace during talks on the US-backed roadmap.
Israeli Prime Minister Ariel Sharon demanded his Palestinian counterpart Mahmoud Abbas begin to crack down on militants as set out in the peace plan, his office said.
Mr Abbas said in a statement that the Jerusalem talks had been "beneficial and productive" but also called on Israel to implement a long list of demands.
The meeting - which lasted three hours and ended at about midnight local time (2100 GMT) - was the first between the two men since Mr Sharon persuaded his cabinet to approve the so-called peace roadmap.
It comes days before they are scheduled to hold a joint session with US President George W Bush in the Jordanian resort of Aqaba.
The prime minister demanded that his Palestinian colleague take vigorous action to halt terrorism
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"The prime minister demanded that his Palestinian colleague take vigorous action to halt terrorism and practical steps on the ground," Mr Sharon's office said in a statement.
Those steps included "dismantling terrorist organisations, arresting terrorists and confiscating illegal weapons" the statement added.
Mr Sharon also renewed his offer to pull Israeli troops out of parts of the Gaza Strip and West Bank, where Palestinian security forces would take charge and round up militants, it added.
Hours before the meeting began, Israeli troops shot dead two Palestinian militants in incidents in the West Bank city of Jenin and in Khan Younis in the Gaza Strip.
'Guarded optimism'
The BBC's Barbara Plett in Jerusalem says that the prime ministers are under pressure from the Americans to come up with a firm action plan to improve the chances success at their three-way summit with President Bush.
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ROADMAP MAIN POINTS
Phase 1 (to May 2003): End to Palestinian violence; Palestinian political reform; Israeli withdrawal and freeze on settlement expansion; Palestinian elections
Phase 2: (June-Dec 2003) Creation of an independent Palestinian state; international conference and international monitoring of compliance with roadmap
Phase 3 (2004-2005): Second international conference; permanent status agreement and end of conflict; agreement on final borders, Jerusalem, refugees and settlements; Arab states to agree to peace deals with Israel
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Raanan Gissin, a spokesman for Mr Sharon, was quoted as saying the Israeli leader approached the meeting with "guarded optimism".
Palestinian Foreign Minister Nabil Shaath said: "We are going [into the talks] because we feel there is an opportunity."
In an interview published on Thursday, Abu Mazen said he expected to reach an agreement with one of the militant groups to halt attacks on Israelis.
"My assessment is that by next week I will arrive at a ceasefire agreement with Hamas," he told the Israeli newspaper Yedioth Aharonoth.
But a senior Hamas official, Abdel Aziz al-Rantissi, said he was not aware any such agreement was planned, Reuters news agency reported.
US intervention
The summit with Mr Bush will be the US president's highest profile intervention in Middle East diplomacy to date.
However, the Palestinian leader, Yasser Arafat, has reminded Israel and the US that he still holds significant power despite efforts to work around him.
Out of favour in Washington, he has not been invited to the summit with Mr Bush and reportedly delayed Thursday's meeting between Mr Sharon and Abu Mazen.
Before the Jordan summit, Mr Bush will meet Arab leaders in the Egyptian Red Sea resort of Sharm el-Sheikh.
Israel has welcomed news of Mr Bush's intervention.
"President Bush would not bother to help if he didn't think it was possible to renew negotiations in this summit," Israeli Foreign Minister Silvan Shalom said.
"I very much hope that we will leave there with a decision to renew talks," he said.