United Nations Secretary General Kofi Annan has said he is encouraged following talks with Palestinian and Israel leaders.
Mr Annan is on his first trip to the region in four years
Mr Annan held talks with Palestinian leader Mahmoud Abbas, a day after meeting the Israeli prime minister.
He is trying to promote the stalled "roadmap" peace plan, which envisages a viable Palestinian state alongside a secure Israel.
Mr Abbas has said he hopes militants will agree to a ceasefire this week.
Meanwhile, Israel said it would remove 24 unauthorised West Bank outposts.
A complete cessation of Palestinian violence and the dismantling of Israeli outposts built after March 2001 are key requirements of the internationally backed roadmap plan, which has been revived since Mr Abbas was elected earlier this year.
"I think that the possible developments give us a chance to re-energise the [peace] process," Mr Annan said in the West Bank town of Ramallah.
Mr Annan earlier placed a wreath by the grave of late Palestinian leader Yasser Arafat.
As he went into the talks with Mr Abbas, hundreds of Palestinians held a demonstration against Israel's controversial West Bank separation barrier.
Mr Abbas and Israeli Prime Minister Ariel Sharon agreed a ceasefire at a summit in the Egyptian resort of Sharm al-Sheikh in February, but militant Palestinian groups have not formally joined the truce.
Two weeks after the Egyptian summit, a Palestinian suicide bomber attacked a nightclub in Tel Aviv.
Mr Abbas told Israeli TV on Sunday night that a meeting of all the Palestinian factions in Cairo on Tuesday could result in a ceasefire declaration.
"God willing, we will go there to declare a ceasefire... for the sake of giving the peace process a chance to begin and to return to its normal path," he said.
He said the truce could continue "as long as the situation moves in a positive direction".
Hopes for peace have been renewed since Mr Abbas was elected Palestinian leader following the death of Arafat.
Mr Sharon had refused to negotiate with Arafat, branding him an obstacle to peace. He instead came up with a unilateral plan to withdraw Israeli settlers from the Gaza Strip.
Mr Sharon (left) said Israel would abandon some West Bank outposts
The disengagement plan is due to go ahead in July.
Under the plan, all 8,000 settlers will leave Gaza, as well as the troops that protect them. Israel will maintain control of Gaza's borders, coastline and airspace.
Mr Annan met Mr Sharon in Jerusalem on Sunday, shortly after the Israeli cabinet offered to dismantle 24 unauthorised West Bank outposts.
All settlements in Gaza, the West Bank and East Jerusalem are considered illegal under international law, though Israel disputes this.
Israeli Defence Minister Shaul Mofaz and Palestinian Interior Minister Nasser Yousef will meet on Monday evening to discuss the delayed handover of five West Bank towns.
Israel agreed at the Sharm al-Sheikh summit to cede control of the towns of Qalqilya, Tulkarm, Jericho, Bethlehem and Ramallah to Palestinian security forces.
But the effort has become bogged down in a disagreement over the dismantling of Israeli checkpoints outside Jericho.