The first direct negotiations to end a three-week stalemate between Israeli forces and armed Palestinians barricaded in one of Christianity's holiest shrines ended Tuesday with both sides citing progress and pledging to continue talking.

Prime Minister Ariel Sharon, meanwhile, told an American Jewish group he believed a U.S.-sponsored international peace conference could end Mideast hostilities. He credited the Israeli incursion into the West Bank with creating the climate for a settlement.

"Regional peace is within our grasp," Sharon said. "I am optimistic about the future."

Palestinians had been optimistic for a quick resolution in the talks to end the standoff at the Church of the Nativity. But the key dispute remained. Israel says wanted militiamen inside the Church of the Nativity must be tried in Israeli courts or exiled abroad; the Palestinians propose sending them to the Gaza Strip under international escort.

Palestinian lawmaker Salah Tamari, who participated in the talks, said both sides were determined to reach a peaceful solution. Israel, he said, had agreed to evacuate four sick people from the church compound. He did not say if they were civilians, armed Palestinians or the clerics who have been inside since April 2.

"The meeting was positive and constructive, but we didn't reach any agreement," Tamari said.

Gadi Golan, head of religious affairs division at the Israeli foreign ministry, said he had not yet been briefed on the result of the day's talks, which were handled by an all-military team. Army spokesman Lt. Col. Olivier Rafowicz declined to comment, and his office would only say progress had been made and talks would continue.

Bethlehem Mayor Hanna Nasser called the meeting "important." Tamari said the Gaza proposal "was discussed as an option." Beyond that, he would only say delegates needed to consult with the Palestinian leadership before talks resumed Wednesday.

With the Israeli incursion significantly scaled back, gruesome street scenes played out as masked Palestinian militiamen summarily executed fellow Palestinians accused of collaborating with Israel. Three men were shot dead in Hebron, and two of the bullet-riddled bodies were strung up by a mob.

The killings were carried out to avenge the Monday night Israeli killing of Marwan Zalloum, commander of the Al Aqsa Martyrs' Brigade in Hebron.

"The fate of all collaborators will be like this," a masked militiaman, wearing an Al Aqsa headband, said before he and six others sped away.

Late Tuesday, Israeli forces shot and killed three armed Palestinians who tried to infiltrate the Jewish settlement of Netzarim in central Gaza, the military said. Such infiltration attempts have been reported almost daily over the past two weeks.

An explosion also rattled the Ramallah headquarters of Palestinian leader Yasser Arafat. Tawfik Tirawi, head of Palestinian intelligence, said Israeli troops tried to destroy a wall between the prison inside the compound and Arafat's office. The army said the blast was the controlled destruction of grenades found in the compound.

In Bethlehem, where about 230 armed Palestinians, including about 30 militiamen, forced their way into the Church of the Nativity. Palestinians proposed during a first round of negotiations to take the wanted men to the Gaza Strip under international protection.

Several dozen Palestinian civilians, as well as priests and nuns, also are in the church compound, built over the grotto where tradition holds Jesus was born.

Nasser, who also participated in a first round of talks earlier Tuesday, had said Israeli negotiators had not rejected the Palestinian plan outright.

Golan said Israel only would accept a resolution based on its offer to exile the gunmen or put them on trial in Israel. Palestinians have reject that.

After the opening round of talks, the Vatican news service Fides reported from Rome that the Palestinian proposal called in part for disarming gunmen in the church and taking them to Gaza under international guarantees offered by the Red Cross, the Vatican and the United States.

Senior Israeli military officials identified eight wanted suspects inside the church, including seven activists in the Al Aqsa, a militia affiliated with Yasser Arafat's Fatah organization.

In his remarks by satellite link to the American Israel Public Affairs Committee in Washington, Sharon said Israel would pursue a three-point policy if a U.S. peace conference were held. First, he said, there must be a cessation of violence and incitement to attack Israel. Then, he said, Israel would be prepared for a long-term armistice with the Palestinians. In a third stage, Israel and the Palestinians would reach a final settlement.

He said borders would be drawn, implying his approval of a Palestinian state, which President Bush has been urging.

At the shooting of alleged Palestinian collaborators in Hebron, a large crowd, including children, gathered at the scene. Some of the bystanders took one of the bloodied victims and strung him, head down, on an electricity pylon. One boy climbed up to help with the hanging.

A day earlier, gunmen from the same militia, fired round after round into three accused collaborators in a downtown Ramallah square. One died as some bystanders tried to prevent ambulances from approaching the men writhing on the ground in pain.

On the political front, a senior Israeli government official, speaking on condition of anonymity, told foreign correspondents Israel was interested in last month's Arab League peace initiative. The official said there was some hope the Arab world, negotiating on behalf of the Palestinians, would be more flexible than Arafat.

In March, the 22 Arab League nations adopted a Saudi initiative offering pan-Arab acceptance of Israel and with normal relations after Israel returns all Arab land seized in the 1967 Mideast war. The deal also requires Israel to accept a Palestinian state with east Jerusalem as its capital and an adequate resolution of the problem of Palestinian refugees.