Associated Press Palestinian Yousef Alwhedi sits in front of his family home alongside the road to the Jewish settlement of Netzarim, which was bulldozed by Israeli troops in the village of Mograka, Gaza Strip. The home was bulldozed last week following the destruction nearby of an Israeli Merkava-3 tank by explosives planted by Palestinian militants.

JERUSALEM - Israel and the Palestinians were making progress toward a cease-fire, and it appeared Israel might withdraw its troops from the West Bank town of Bethlehem as early as yesterday night - meeting an important Palestinian demand for a truce in the 18-month-old Mideast conflict.

Vice President Dick Cheney arrived to bolster the efforts of U.S. mediator Anthony Zinni, and the two Americans held talks yesterday afternoon with Israeli Prime Minister Ariel Sharon.

The effort follows one of the bloodiest periods in the Israeli-Palestinian conflict. Israelis are increasingly impatient for an end to the carnage, while the Palestinians have been suffering very heavy casualties and economic losses.

In violence yesterday, Israeli soldiers shot and killed an armed Palestinian near a crossing point between Gaza and Israel, the military said. Also, Palestinians fired two Qassam rockets into Israel from northern Gaza, the military said. Palestinians said Israel sent armored vehicles to search farms afterward.

Meanwhile, Israeli soldiers tracked down and arrested two Palestinians who had infiltrated northern Israel planning to carry out a terror attack, the military said.

In the most promising sign since Zinni arrived last week, Israeli and Palestinian security officials met three times in less than 24 hours, and officials on both sides said they expected a troop pullback from the Bethlehem area. After nightfall, soldiers began dismantling rooftop positions there, witnesses said.

"The meeting today was tough and serious but positive," said Jibril Rajoub, the Palestinian security chief in the West Bank. "The Israelis are committed to withdrawing from all (Palestinian-run) areas in the West Bank."

An Israeli official, speaking on condition of anonymity, said the withdrawal was expected yesterday night.

Israeli forces have entered more than a half-dozen Palestinian towns and cities this month in a search for Palestinian militants. They have withdrawn from all the Palestinian population centers except Bethlehem and Beit Jalla, two adjacent West Bank towns just south of Jerusalem.

It was not clear whether Israeli troops would remain in a few Palestinian-run areas of the Gaza Strip - a key road and some farmland - which they also seized in recent months, and this was apparently not part of yesterday's emerging deal.

An Israeli pullout would meet the most immediate Palestinian demand for reaching a cease-fire. However, any breakthrough could be swiftly undone by Palestinian attacks on Israelis, which could prompt Israeli retaliation.

Zinni, who has been shuttling between Israeli and Palestinian leaders, is trying to get the two sides to implement a cease-fire deal brokered last year by CIA chief George Tenet.

Both sides previously endorsed the plan, which calls on the Israelis to pull back troops to where they were before the fighting began in September 2000. The Palestinians must prevent attacks against Israel and - in what may prove to be a huge undertaking - collect weapons from militants.

Several previous cease-fire efforts have failed, and even if the two sides strike a deal there's no guarantee it will hold.

Many Palestinian militants say the only way they can win concessions from Israel is by fighting. And many Israelis believe Sharon should take an even tougher line and step up military operations against the Palestinians.

Both sides see Cheney's presence as an incentive to reach a truce deal.

Upon arriving, Cheney met Sharon and said he was seeking to revive Israeli-Palestinian talks with an aim of reaching a full-blown peace treaty based on U.N. resolutions. The vice president said both sides would have to take steps to end violence and improve the atmosphere for peace talks.

"We continue to call upon Chairman (Yasser) Arafat to live up to his commitment to renounce once and for all the use of violence as a political weapon and to observe a 100 percent effort to stamp out terrorists," Cheney said.

"In that same spirit, I will be talking to Prime Minister Sharon about the steps that Israel can take to alleviate the devastating economic hardships being experienced by innocent Palestinian men, women and children," he added.

Sharon compared the U.S. campaign against international terrorism to Israel's battle against Palestinian attackers.

The Palestinians reject this analogy, saying they are resisting 35 years of Israeli military occupation in the West Bank and the Gaza Strip, with the aim of establishing an independent Palestinian state.

Cheney has set aside time to meet with the Palestinian side, aides said, although no specific meetings have been scheduled. A meeting with Arafat was a possibility, a senior U.S. official said.

Palestinian parliament speaker Ahmed Qureia said that if Cheney chose not to meet Arafat he would not be received by any other Palestinian official.

Also yesterday, supporters of the Palestinian Islamic Jihad organization vowed to keep up attacks.

At a rally in the northern Gaza Strip town of Beit Lahia, demonstrators chanted "Death to Israel. Death to America," and "No to surrender, yes to holy war."

"Our fighters will terrorize our enemy everywhere by all means," one masked activist told the crowd of about 600.

Since fighting erupted in September 2000, 1208 people have been killed on the Palestinian side and 352 on the Israeli side.