Israel might allow Palestinian leader Yasser Arafat to leave the West Bank city of Ramallah for the first time in more than a year, Ariel Sharon has reportedly said.
The two men met in a carefully choreographed event
He made the offer to Palestinian Prime Minister Mahmoud Abbas during two hours of talks following a carefully managed joint appearance in Jerusalem.
The two leaders also agreed to set up a number of joint working groups to try to press ahead with the US-backed peace plan known as the roadmap.
Their talks were set to be followed by a major confidence-building measure: the withdrawal of Israeli troops from the West Bank town of Bethlehem on Wednesday.
Enough killing, enough tragedy, enough pain - let's move forward with courage to the future we all deserve
Palestinian Prime Minister
In their highly symbolic joint appearance, Mr Sharon and Mr Abbas - also known as Abu Mazen - shared an enthusiastic handshake and said their people held no fundamental enmity towards each other.
The most public meeting between the two men since Abu Mazen took office at the end of April included no Palestinian or Israeli flags - but did feature Cabinet ministers from the two sides chatting amicably.
There were sporadic incidents of violence in the 48 hours before the meeting began on Tuesday afternoon, but a tenuous ceasefire between the two sides seemed to be holding.
ROADMAP MAIN POINTS
Phase 1 (to May 2003): End to violence against Israelis and Palestinians; 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
Speaking before the meeting, Mr Sharon reiterated his promise to make painful concessions to achieve peace, but warned that his primary responsibility was for the safety of his people.
"There will be no compromise with terror. There will be no peace with terror," he said.
Abu Mazen said that through dialogue, the two sides could put the past behind them.
"Every day that passes without an agreement is a lost opportunity. Every person killed is a tragedy," he said.
"So enough killing, enough tragedy, enough pain. Let's move forward with courage to the future we all deserve," he said.
In public, the two men avoided difficult issues including settlements, refugees and the status of Jerusalem.
But in the closed-door meetings, they agreed to set up joint committees on four subjects: Palestinian prisoners in Israeli jails, trade, security and incitement.
Mr Sharon also reportedly offered to let Mr Arafat leave Ramallah for Gaza if he requests.
But there were broad hints from the Israeli side that Mr Arafat might not be allowed to return to the West Bank if he did leave.
The BBC's James Reynolds in Jerusalem says Mr Arafat might have little to gain by trading virtual confinement in one place for confinement in the other.
Earlier on Tuesday, Israeli troops shot dead a Palestinian gunman who attacked an army checkpoint in the West Bank, an army spokesman said.
The shooting, near the city of Tulkarm, is the second blamed on Palestinians since the main militant groups declared a ceasefire on Sunday.
The al-Aqsa Martyrs' Brigades have not agreed to observe to the ceasefire.
Ahead of his meeting with Mr Sharon, Abu Mazen told the Palestinian legislature that they would tackle the issues of Jewish settlements, Israel's policy of killing top militants, and restrictions on movement in Palestinian areas.
He reportedly said he expected Israeli troops to withdraw from all areas occupied since September 2000 within six weeks.
The US peace plan for the region requires Israel to return control of Palestinian areas to the Palestinian Authority.
Israel has already withdrawn from parts of the Gaza Strip.