JERUSALEM -- Israel agreed to return the West Bank town of Bethlehem to Palestinian control after its pullback Monday from the Gaza Strip, crucial steps that advance a U.S.-backed "road map" to Palestinian statehood and raise hopes that 33 months of violence may be nearing an end.
The two sides' prime ministers also set a meeting to plan their next moves, as bulldozers tore down Israeli checkpoints and traffic flowed freely in Gaza for the first time in months. Palestinian police took control of the Gaza town of Beit Hanoun on the heels of the departing Israeli troops.
The developments followed declarations of a temporary halt to attacks by three main Palestinian groups, but there were still trouble spots.
The first full day of the truce was marred by a Palestinian shooting that killed a Bulgarian construction worker on an Israeli road project near the West Bank town of Yabed. Renegade members of the Al Aqsa Martyrs' Brigades, loosely linked to Yasser Arafat's Fatah movement, claimed responsibility.
Palestinian Information Minister Nabil Amr called the killing "an individual attack that should not affect the truce declaration" and said "the Palestinian government will do its best to prevent such attacks" in the future.
Three hours later, Palestinians opened fire on workers building a security fence near the West Bank town of Qalqiliya, the military said. Soldiers returned fire, but no one was hurt.
Despite the violence, Israeli and Palestinian officials remained upbeat about prospects for further advances under the "road map" peace plan launched by President Bush at a June 4 Mideast summit. The plan leads through three stages to a Palestinian state in 2005.
Israeli Prime Minister Ariel Sharon declined to criticize his Palestinian counterpart, Mahmoud Abbas, after the shootings, noting that security responsibility was handed over to the Palestinian Authority in the northern Gaza town of Beit Hanoun only on Monday morning.
"Even if the Palestinians were the fastest in the world, and the most determined, you can't expect them to destroy terrorism in a moment," he told members of his Likud parliamentary caucus. In the past, Sharon has made strident demands on the Palestinians to crack down immediately on militants.
Sharon planned to meet with Abbas in Jerusalem on Tuesday to discuss the way forward.
Security measures to be taken by both sides were expected to figure prominently in the talks, along with Palestinian demands for the release of political prisoners and further Israeli withdrawals from territory reoccupied since the start of fighting in September 2000.
In a statement Monday, Abbas said the success of the peace plan "depends on carrying out the commitments of both sides." He called on the Israelis to implement their part of the plan.
Israel agreed to withdraw from Bethlehem on Wednesday, Palestinian security sources said. Israeli military sources, speaking on condition of anonymity, would confirm only that the handover was to take place toward the end of the week.
Late Sunday, Israeli troops rolled out of Beit Hanoun in line with the road map, which calls on Israel to withdraw to positions it held before the outbreak of hostilities nearly three years ago.
A long convoy of blue Palestinian police cruisers moved into the area at dawn, confronting a scene of devastation -- smashed overpasses, pockmarked roads, pulverized homes and thousands of uprooted orange trees.
"You were late," 65-year-old Mohammed Shabat told them, pointing to the destruction. "But, God willing, we will bring this town back to the old days."
Israeli troops had moved in and out so many times that it became routine, as they tried to stop Palestinian militants from firing homemade rockets over the fence at the Israeli town of Sderot, less than a mile away.
Later in the morning, Israel dismantled checkpoints along the main north-south roads, which had been a major cause of hardship. Palestinian motorists trying to get from one end of Gaza to the other had often waited for hours at the barriers. The road was frequently closed, following Palestinian attacks on soldiers and Jewish settlers.
In the mid-1990s, Israeli troops pulled out of Palestinian population centers as part of interim peace deals. After fighting erupted again, Israel reoccupied most of those areas.
Two new ingredients have raised hope for the current cease-fire effort: both sides, exhausted by the carnage, are grateful for the break in fighting, and the United States is intensively engaged in supervising implementation of the road map.
Over the weekend, National Security Adviser Condoleezza Rice held talks with Israeli and Palestinian leaders on how to move forward.
On Sunday, the three major Palestinian factions -- Hamas, Islamic Jihad and Fatah -- announced a suspension of attacks. The two Islamic militant groups agreed to lay down arms for three months, while Arafat's secular Fatah announced a six-month truce.
Israeli officials reacted coldly to the Palestinian truce announcements, which were accompanied by a number of demands, including a prisoner release and a halt to all Israeli military strikes.
"The cease-fire agreement (with the militants) was not reached with Israel," Israeli Foreign Minister Silvan Shalom said Monday. "Since we are not party to it, its conditions are none of our business."
While refusing to make blanket promises, Israel has pledged to halt targeted attacks of wanted Palestinians in areas now controlled by Palestinian police.
Sharon said he has also instructed the Shin Bet security service to prepare a list of Palestinians who could be freed without harming Israel's security.
Human rights organizations say Israel is holding about 5,000 Palestinians on security-related charges, of whom around 1,000 are held in "administrative detention," allowing indefinite imprisonment without trial.
Shalom reiterated Israeli demands that "the Palestinian Authority dismantle the terror organizations."
A senior security source told The Associated Press that this meant confiscating the militants' weapons, destroying bomb factories and arresting anyone trying to carry out attacks.
However, in an important nuance, he added that Israel would no longer demand arrest of leaders or militants who carried out attacks in the past.