Hours after Secretary of State Colin Powell demanded "a clear statement from Israel that they are beginning to withdraw," Israeli forces began withdrawing early Tuesday from two of the West Bank cities they had occupied, Palestinian security sources said.

Tanks were rumbling out of Tulkarem and Qalqiliya as troops left buildings and schools after about a week's occupation, Palestinian security sources said, speaking on condition of anonymity.

"It's a start," White House press secretary Ari Fleischer said in Washington. "As the president said ... all parties in the Middle East have responsibilities and the president expects all parties to step up to them."

Shortly after the pullout started, troops and tanks began a fresh incursion into the southern West Bank town of Dora, witnesses said.

Tanks and armored personnel carriers rolled into the town before dawn as helicopters provided cover from the air. The sound of gunbattles could be heard, witnesses said.

A statement issued by Defense Minister Binyamin Ben-Eliezer late Monday night said that the operation to wipe out militant networks in Qalqiliya and Tulkarem had been successful.

As Israel announced the limited pullback, its forces pushed deeper into other Palestinian strongholds Monday in house to house fighting backed by helicopters and bulldozers.

Although troops were leaving the two northwest towns, there was still a heavy Israeli presence in the major West Bank cities of Ramallah, Bethlehem, Nablus, and Jenin.

Hours after Powell insisted on a response to U.S. demands for an Israeli withdrawal, the Defense Ministry said the staggered pullback from Qalqiliya and Tulkarem was planned for early Tuesday.

Nevertheless, Prime Minister Ariel Sharon pledged to continue the 12-day-old offensive he launched in response to a wave of suicide bombings.

Powell said he was encouraged but hoped the moved would not be "a little bit of this and a little bit of that," with advances in some areas and pullbacks in others.

Monday's developments unfolded as Powell arrived in Morocco on the first stop of his peacemaking mission and was bluntly told by King Mohammed: "Don't you think it was more important to go to Jerusalem first?"

World oil prices spiked as much as 6 percent in a fresh wave of anxiety after Iraq said it was halting crude exports for 30 days to demonstrate support for the Palestinians. National Security Adviser Condoleezza Rice said it would not deter Bush from seeking the Iraqi leader's ouster.

"We ought to remind them that they're going to have a hard time eating their oil," Rice said in a speech in Texas, suggesting that Saddam needs money from oil exports more than the United States needs Iraq's oil.

At Bethlehem's Church of the Nativity, fire broke out in the compound during a gun battle between Israeli soldiers and more than 200 armed Palestinians holed up inside, and the violence threatened the delicate ties between the Vatican and the Jewish state.

In the West Bank's largest city, Nablus, dozens of gunmen surrendered to Israeli troops while scores more lay wounded on blankets on a mosque floor. Some of the men were dying, and doctors lacking even the most basic supplies operated on others without anesthetics.

Israeli helicopters also pounded the Jenin refugee camp with missiles, and bulldozers flattened homes as gunmen retreated. Israeli officials estimated more than 100 Palestinians have been killed in the camp in recent days.

Israeli Brig. Gen. Eyal Shline said the armed men "seem to have decided to fight to the last, to make the battle as bloody as possible," and that several blew themselves up in suicide attacks on soldiers.

Addressing Parliament, Sharon said Israel's assault was a response to a "murderous insanity which has taken hold of our Palestinian neighbors."

He accused Palestinian leader Yasser Arafat of heading a "regime of terror" and said Israel would press on "until it has dismantled Arafat's terror infrastructure and the murderers hiding in different places have been arrested."

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

Sharon appeared to be suggesting he would only do business with Palestinians not affiliated with the Palestinian Authority.

Palestinian reaction was angry. Cabinet Minister Saeb Erekat said Sharon's "endgame all along was to dismantle the Palestinian Authority," and that Israel would not find Palestinians to go along with such a plan. Erekat said Sharon was defying the United States by refusing to stop the offensive immediately.

In Jerusalem, U.S. envoy Anthony Zinni met with Sharon. U.S. officials said he restated demands for an immediate withdrawal from the Palestinian territories.

Sharon told Zinni that Israel must remain in the areas until the anti-terror campaign is completed to prevent a return of suicide bombers, said Sharon adviser Danny Ayalon. However, Ayalon said, withdrawals would begin soon.

Palestinian residents of Qalqiliya and Tulkarem, the two cities troops were leaving, had offered relatively little resistance to the Israeli occupation. Militants in other cities, such as Jenin and Nablus in the north, have been battling Israeli forces for several days.

Israeli tanks and troops continue their siege on Arafat's office in Ramallah, preventing people from entering and leaving.

There was a widespread feeling in Israel that the timing of Powell's trip — he will not reach Israel until late this week — and some wording used by U.S. officials suggested an acquiescence with continuing the offensive for a few more days.

Israeli troops and tanks rumbled into the West Bank on March 29, beginning a hunt for weapons, explosives and militants who have terrorized the country with suicide bombings and other attacks.

More than 1,500 Palestinians have been arrested by Israel since then, 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 and uncovered 15 labs for making explosives, the officials said.

Before daybreak Monday, Israeli attack helicopters began firing missiles at the Jenin camp after militants ignored calls to surrender. Jamal Abdel Salam, a resident and activist in the Islamic militant Hamas group, said army bulldozers flattened homes, and dozens of houses were destroyed.

By early afternoon, Israeli forces controlled almost the entire camp, the army said. The military said about 150 men put down their weapons and emerged early Monday, but Abdel Salam said only women, children and the elderly left the camp. The militants were ready to fight to the death, he said.

Two Israeli soldiers were killed in the camp Monday, the military said.

In Nablus, smoke rose from the Old City, a densely populated maze of stone buildings and narrow streets. Army officials said troops controlled about half the Old City, and that dozens of gunmen surrendered Monday.

In Bethlehem, Israeli troops ringing the Church of the Nativity exchanged fire with some of the Palestinians who have been inside for seven days.

A senior Israeli army officer, speaking on condition of anonymity, said two border policemen who were shot and wounded by Palestinians threw a smoke grenade into the compound, sparking a fire.

The fire burned for about an hour in a second-floor meeting hall above the courtyard of St. Catherine's, a Roman Catholic church adjacent to the Church of the Nativity. It destroyed a piano, chairs, altar cloths and ceremonial cups, clerics said. Israeli troops searched Palestinian firefighters who came to extinguish the blaze, but eventually let them put out the fire by spraying water over the compound's wall.

Sharon told Parliament that soldiers would surround the church until the gunmen surrender. The Franciscans, meanwhile, accused Israel of violating a pledge not to attack the church. Church officials said the clerics were not hostages and would stay in the compound.

The Associated Press contributed to this report.