Israeli tanks rolled into the West Bank city of Hebron early Thursday, firing in all directions, and a senior Israeli military official sounded an optimistic tone about prospects for peacefully ending a three-week standoff at Bethlehem's Church of the Nativity.

Israeli and Palestinian negotiators were to meet again Thursday, after both sides reported slight progress in the second straight day of talks Wednesday. They agreed to allow 10 to 15 youths, including two 10-year-olds, to leave the church compound, and Israeli forces also were to take out the bodies of two dead Palestinians, officials from both sides said.

"There is very cautious optimism that the affair is closer to an end today than it was yesterday," the Israeli army spokesman, Brig. Ron Kitrey told Israel's army radio Thursday. "There is an intention to allow several people to get out of there."

Two Palestinians inside the Church of the Nativity compound were shot Wednesday and one of them died as Israeli and Palestinian negotiators gathered next door for the second round of talks to end the standoff at one of Christianity's holiest sites.

More than 200 Palestinians, many of them armed, fled into the church compound, built at the biblical site of Jesus's birth, ahead of invading Israeli forces on April 2. The Palestinians proposed they be escorted to Palestinian-controlled Gaza. Israel has been demanding they surrender or accept deportation.

"We think that this is a very reasonable offer, and we hope that the negotiations ... will produce a resolution to this very important issue," said government spokesman Arye Mekel.

The Bethlehem invasion was part of a massive Israeli military operation that began March 29 with the aim of dismantling Palestinian militias behind deadly attacks on Israelis.

Maj. Gen. Giora Eiland, head of the military's planning branch, told The Associated Press that in the West Bank "almost the entire leadership" of Hamas, Islamic Jihad, and Al Aqsa Martyrs' Brigade, a militia linked to Palestinian leader Yasser Arafat's Fatah movement, had been killed or arrested. But Eiland said they could rebuild, and the relative lull in attacks "might not last years or even months."

Israel has said the operation is over, but that its troops would remain in Bethlehem until the church standoff is over and around Arafat's compound until he surrenders men inside the compound who are wanted by Israel. Forces also frequently move in and out of other West Bank towns and villages, making arrests.

Witnesses said about 10 tanks and 10 armored vehicles entered Hebron from one direction early Thursday. Soldiers exchanged fire with armed Palestinians and made some arrests before pulling out less than two hours later, they said. The army said its special forces were operating in the area and had arrested a Fatah activist.

Ahmed Bashir, a member of the Force 17, an elite security unit, was killed and at least four Palestinians were wounded, Palestinians said. Hebron had been left alone during Israel's West Bank offensive, except for occasional brief incursions.

In Gaza, which was spared during the operation, Israeli soldiers shot and killed four Palestinians who tried to infiltrate the Jewish settlement of Kfar Darom early Thursday, the military said. Palestinian security sources said Israeli forces later entered 300 yards into Palestinian territory adjoining the settlement, and doctors said a Palestinian police officer was killed in the ensuing exchange of fire.

The day before, the militant Hamas group issued an unusual appeal, calling on children not to try to infiltrate Jewish settlements. The call came after Israeli soldiers shot and killed three Palestinians trying to break into the settlement of Netzarim in central Gaza on Tuesday. Palestinians said two of them were 14 years old and the third was 13.

Also on Thursday, a Palestinian approached an Israeli roadblock in a car and blew it up as he tried to escape on foot, the military said. Soldiers shot and killed him.

At least seven Palestinians were killed Wednesday, one at the Church of the Nativity and two in an Israeli military raid near Hebron. A teen-age boy was killed when students clashed with soldiers carrying out arrests near their school in Jabaa village and three Palestinians died in an apparent bomb-making accident in the Gaza Strip.

Israel dispatched a team of officials to the United Nations early Thursday to meet with U.N. officials about a fact-finding mission into the battle at the Jenin refugee camp in the northern West Bank, Israeli officials said. Israel is unhappy with the composition of the team and demands it examine not only the weeklong battle in the camp, but also the Palestinian terror infrastructure there.

The three members of the team met in Geneva before their planned trip to the Middle East. Rejecting Israel's demand for a delay, U.N. Secretary-General Kofi Annan ordered to team to arrive by Saturday.

Palestinians charged that Israeli forces massacred hundreds of people in the Jenin camp, while Israel said the Palestinian casualties were in the dozens, and most of the dead were gunmen or bombers. About 50 bodies have been recovered.