NABLUS, West Bank ? Under heavy U.S. pressure, Israel withdrew Tuesday from two Palestinian towns, but soldiers invaded other areas of the West Bank and fought dozens of beleaguered gunmen in a refugee camp in what was emerging as the deadliest battle of the 12-day military offensive.

Several Israeli armored vehicles drove into the West Bank town of Hebron on Tuesday, but witnesses said they later turned back. It was not immediately clear whether it was part of a brief incursion or the beginning of a takeover of another major Palestinian town.

However, Israel agreed to briefly ease the confinement of Palestinian leader Yasser Arafat and permit him to meet with four senior advisers ahead of a cease-fire mission by Secretary of State Colin Powell who is due to arrive Friday.

Yet Israel said Arafat’s isolation would continue. In a speech to parliament Monday, Israeli Prime Minister Ariel Sharon branded Arafat the head of a “regime of terror” Israel would have to dismantle, and suggested he would no longer do business with Arafat and other members of his Palestinian Authority.

Arafat’s continued isolation could complicate Powell’s mission, since Palestinians have said they would boycott cease-fire efforts if Arafat was bypassed by the secretary of state. Israeli Defense Minister Binyamin Ben-Eliezer met Tuesday with U.S. envoy Anthony Zinni, in preparation for Powell’s arrival, and Palestinian officials said they expected to hold talks with Zinni in the coming day.

In Knoxville, Tenn., President Bush said Monday that Mideast peace will require leadership by both sides.

“The United States is firmly committed to achieving peace,” Bush said. “I meant what I said about withdrawal without delay, and I mean what I say when I call upon the Arab world to strongly condemn against terrorist activities.”

Just hours after Bush’s stern call for a withdrawal, Israeli forces pulled out of the West Bank towns of Qalqiliya and Tulkarem early Tuesday, but troops remained in the towns of Nablus, Bethlehem, Jenin and Ramallah. Sharon said Monday that the offensive would continue until Palestinian militias responsible for a string of shooting and bombing attacks on Israelis were crushed.

The deadliest fighting raged Tuesday in the Jenin refugee camp, where dozens of gunmen remained holed up in a small area.

Camp resident Jamal Abdel Salam said he was told by the armed men that they were being surrounded by Israeli soldiers in the eastern part of the camp.

“They said they prefer death to surrender. They asked me to look after their families,” Abdel Salam, an activist in the Islamic militant Hamas group, said in a telephone interview.

Israeli commanders in the area have said several Palestinian gunmen with explosives strapped to their bodies have blown themselves up in suicide attacks. So far, nine Israeli soldiers have been killed in more than a week of fighting in the camp, and estimates by both sides said more than 100 Palestinians have died. An exact count was not possible because Israel barred reporters and medics from the camp.

The Association for Civil Rights in Israel said dozens of bodies were piled in the streets of the camp and residents were prevented from getting food and water. In a complaint to Ben-Eliezer, the Israeli organization said the military has committed serious human rights violations in the camp, including the demolition of homes with residents still inside. “Those who left their houses to try to get supplies were shot at by the army,” the organization wrote.

There was no immediate response from the Defense Ministry.

In Nablus, the West Bank’s largest city, troops took control of the densely populated downtown area, or casbah, after several days of fierce resistance by Palestinian gunmen. At least 41 Palestinians have been killed in the fighting, but the toll was not final because some bodies were still lying in the streets, medics said.

The military said it has found 16 bomb-making labs in Nablus. Troops rounded up young Palestinian men at a Nablus school, releasing some after brief questioning and putting others on large trucks, apparently to be driven to detention centers.

On Tuesday afternoon, seven Israeli tanks and two armored vehicles drove several hundred yards into Hebron, one of two major West Bank towns not targeted in the Israeli offensive that began March 29. However, the Israeli convoy turned back after a brief spin, witnesses said.

Israeli forces also raided the small town of Dura, south of Hebron. Palestinian security officials said Israeli forces leveled compounds of the Palestinian military intelligence and the Force 17 security service. Two Palestinians were killed in exchanges of fire with Israeli forces, the security officials said. Males between the ages of 15 and 40 were rounded up for questioning, witnesses said.

Initially, some Israeli officials said that “Operation Defensive Shield” might last four to eight weeks, and Israel has yet to say when forces will leave the West Bank towns it still occupies. Israel’s deputy defense minister, Dalia Rabin-Pelossof, said that in cutting short the operation, Israel was responding to U.S. pressure.

“Even when we talked about a longer timetable, at least the army did, we knew the sands of political time were running out and then the Americans came, with their interests, and proclaimed yesterday the unequivocal request by the president of the United States that we begin withdrawing, and therefore a decision was taken” to leave Qalqiliya and Tulkarem, Rabin-Pelossof told Israel Radio.

Troops pulled back to the outskirts and maintained a tight cordon around the two towns. Ben-Eliezer, the defense minister, said the military offensive, which began March 29, has “dealt a heavy blow to the terrorist infrastructure” in the cities, where weapons were seized and wanted militants were arrested. In Washington, White House press secretary Ari Fleischer offered cautious encouragement for the pullout plans. “It’s a start,” he said.

Meanwhile, a standoff continued in Bethlehem, where Palestinian gunmen were holed up in one of Christianity’s most sacred sites, the Church of the Nativity, built over the traditional birthplace of Jesus. The siege appeared to be straining delicate relations between Israel and the Vatican.

Christian leaders called on Israel to leave Bethlehem after a gunbattle and fire erupted Monday around the church. Some church officials, including a Franciscan friar who briefed the Vatican on the situation, angrily accused Israel of provoking the unprecedented violence around the shrine.

A senior Israeli army officer said two Israeli border policemen, wounded when they came under fire from Palestinian gunmen inside the compound, had thrown a smoke bomb that sparked the blaze. Sharon said Israel would not lift the siege until the armed men have surrendered.

Sharon said the massive assault on Palestinian cities was a response to a “murderous insanity which has taken hold of our Palestinian neighbors.” He accused Arafat of leading a “regime of terror” that Israel would dismantle.

Sharon said that after the operation is over, Israeli forces will withdraw to unspecified buffer zones in the West Bank. He added that “the places we leave must have a responsible Palestinian leadership that will take over the areas.”

The comments angered Palestinians. Cabinet Minister Saeb Erekat said Sharon’s “endgame all along was to dismantle the Palestinian Authority” and that Israel would not find Palestinians to agree to such a plan.

More than 1,500 Palestinians have been arrested by Israel since the offensive began March 29, including 500 to 600 fugitives, among them 70 to 80 involved in planning attacks on Israelis, Israeli military officials said. Troops have confiscated 2,000 rifles.