Meanwhile, the first contingent of U.S. monitors who were to supervise implementation of the "road map" peace plan - a team of 10 to 15 officials headed by John Wolf, an assistant secretary of state - were headed to the region Saturday.
But, says CBS News Correspondent Robert Berger in Jerusalem, "They may have little to do: There's nothing to monitor because neither side is implementing the roadmap."
Renewed violence, including a Jerusalem bus bombing by the militant Hamas group and a string of Israeli helicopter raids in Gaza, has claimed 61 lives since the June 4 launch of the road map, which envisions an end to 32 months of violence and the creation of a Palestinian state by 2005.
Despite the worsening situation, behind-the-scenes meetings were continuing.
A high-level delegation of Egyptian security officials planned to arrive in Gaza on Sunday to meet with Hamas officials to discuss a possible end to attacks.
However, Hamas and Islamic Jihad, who broke off cease-fire talks with the Palestinian leaderhsip a week ago, said Saturday they had no plans to halt attacks on Israel.
"The word cease-fire is not in our dictionary," said Abdel Aziz Rantisi, a hard-line Hamas leader. "Resistance will continue until we uproot them from our homeland."
Palestinian security chief Mohammed Dahlan met Saturday night with Maj. Gen. Amos Gilad, a senior Israeli defense official, at the home of the U.S. ambassador, the Israeli newspaper Haaretz reported on its Web site. The purpose was to discuss an Israeli proposal to withdraw from parts of the Gaza Strip to positions held before the outbreak of fighting in September 2000.
It was the first security meeting since the road map was launched by President Bush and the Israeli and Palestinian prime ministers in a Jordan summit on June 4.
The Saturday meeting might also include Avi Dichter, the head of Israel's Shin Bet security service, and Israeli Defense Minister Shaul Mofaz, Palestinian sources said.
Palestinian Cabinet Minister Yasser Abed Rabbo said that under the latest U.S. proposal, Israel would withdraw from large areas of Gaza and two West Bank cities. The two sides would also make a new cease-fire declaration, Abed Rabbo said.
Israel has repeatedly offered to withdraw from areas it reoccupied in the past 32 months, provided the Palestinians assumed security control.
Palestinian Prime Minister Mahmoud Abbas has said his security forces, badly damaged in Israeli attacks, were not yet prepared for the task, and he wanted to first negotiate agreements with militants on ending attacks against Israelis.
But overnight, the Palestinian leadership met to discuss the proposed pullback and decided it was "ready to take security responsibility in every area the Israelis show willingness to withdraw from," Information Minister Nabil Amr told The Associated Press.
Under the road map, Israel is to withdraw gradually from territory it reoccupied during the recent fighting, while the Palestinians are required to dismantle the militant groups.
Sharon adviser Raanan Gissin said Israel has "submitted a plan ... relinquishing security control over parts of Gaza and handing it over to full control of the Palestinian Authority and Dahlan's security forces."
At the same time, Israel has said it was widening its campaign against Hamas and would target its top leaders.
In recent days, Israel carried out seven missile strikes against Hamas targets, including a failed attempt on Rantisi's life. Hamas blew up a Jerusalem bus to avenge Rantisi, and carried out a number of other attacks.
Violence continued Saturday as Israeli troops shot and killed a 19-year-old Palestinian man, Khaled Saker, when they fired at a group of people throwing stones at them in the Askar refugee camp near Nablus in the West Bank, according to Palestinian hospital officials. Israeli Army officials did not immediately comment.
In Gaza, Israeli forces demolished seven houses and five orange groves in the Rafah area. In recent days, militants had launched mortars from that area at Israeli targets.
The Israeli army said it thwarted a planned suicide attack Saturday and arrested a wanted Palestinian in the West Bank city of Tulkarem. Troops discovered two suicide belts and exploded them, the army said. Hospital officials there said three Palestinian teenagers were lightly wounded in clashes with Israeli troops.
Mideast mediators are planning to meet in hopes of rescuing the peace plan from the quagmire of violence.
Secretary of State Colin Powell and other senior representatives of the so-called Quartet - the United States, United Nations, Russia and the European Union, which together drew up the road map - are to hold talks in Jordan next week.
On Friday, Powell asked Syria, listed by the United States as a sponsor of terrorism, to help quash terrorist acts in the Middle East.
Powell made the request in a telephone call to Syrian Foreign Minister Farouk al-Sharaa. He had made similar appeals to the foreign ministers of Egypt, Jordan and Saudi Arabia a day earlier.
In all the conversations, Powell's message was "to stop the violence, to stop the violent groups," State Department spokesman Richard Boucher said. He said some of those groups, including Hamas, have offices in Damascus.
Also Friday, United Nations Secretary-General Kofi Annan said he would not rule out future deployment of an international armed force to curb violence between Israelis and Palestinians.
Boucher, in response, said third parties could help but it was mostly up to Israel and the Palestinians to stem the violence.