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.

However, Palestinian Information Minister Nabil Amr said it was not clear Fatah was involved. “It was an individual attack that should not affect the truce declaration,” he said, adding that “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 today with Abbas in Jerusalem to discuss the way forward.

In a round of television interviews after Israel pulled troops out of northern Gaza and agreed to withdraw from the West Bank town of Bethlehem, Secretary of State Colin Powell expressed optimism for Mideast peace prospects and boosted Palestinian Prime Minister Mahmoud Abbas as a worthy leader.

“We hope that with these actions, the Palestinian people will realize that Prime Minister Abbas is producing for them and thereby they will empower him even further,” Powell said Monday on CNN’s “American Morning.”