The fence is aimed at keeping suicide bombers out, reports CBS News Correspondent Robert Berger, but the U.S. fears that Israel is drawing a unilateral border.
A barrier would be built east of Ariel — with 18,000 residents the second largest settlement in the West Bank — but would not immediately be connected to the main security fence which runs further west, closer to Israel.
Palestinian officials demanded that the United States stop the construction.
"This (the barrier) is a deliberate attempt by the Israeli government to sabotage President Bush's vision of a two-state solution, to undermine the peace process and to destroy the road map" peace plan, said Palestinian negotiator Saeb Erekat.
The United States wants the barrier to run close to the Green Line, the frontier between Israel and the West Bank before the 1967 Mideast war. The Bush administration has said it might deduct some of the construction cost for the barrier from $9 billion in U.S. loan guarantees to Israel. However, on Tuesday the State Department said it had no immediate plans to cut the guarantees.
In other developments Wednesday, the incoming Palestinian prime minister, Ahmed Qureia, said he has reached agreement on the formation of a Cabinet and would present it to parliament on Sunday and Monday. Qureia would not discuss the size and composition of his new government.
In the West Bank refugee camp of Jenin, Israeli commandos arrested Bassam Saadi, a senior leader of the Islamic Jihad. Witnesses said Saadi was found hiding under a parked car by tracker dogs.
Islamic Jihad vowed to avenge Saadi's capture.
"The enemy will pay a dear price for beating Sheikh Bassam Saadi and for its daily crimes on our people," movement leader Abdallah al-Shami said.
The Israeli Cabinet voted 18-4, with one abstention, Wednesday on the next segments of the security barrier.
About one-fourth of the barrier has already been built in the northern West Bank. In some parts, it runs close to Israel. However, in other areas, the barrier dips further into the West Bank, isolating several Palestinian villages and cutting residents off from their land.
The most contested issue in planning the next segment was whether the barrier would incorporate Ariel, with 18,000 residents the second largest Jewish settlement in the West Bank. Including Ariel on the "Israeli" side would mean the barrier will cut deep into areas the Palestinians claim for a future state.
The Cabinet approved a compromise backed by Prime Minister Ariel Sharon, who hopes to appease both the United States and his hard-line constituents.
Under the plan, the barrier would run east of Ariel, but would not be connected for now to the main security fence running further to the west, closer to Israel. The open sections would be patrolled by soldiers.
"Certainly it (the barrier) has to pass east of Ariel, but in a manner that will not antagonize the (Palestinian) population of the territories and will be in coordination with the agreements we have with the U.S. government," Vice Premier Ehud Olmert said before entering the Cabinet meeting.
The Palestinians charge that Israel is grabbing land and unilaterally drawing a border that should be determined in future peace talks.
Sharon initially opposed construction of the barrier because it would leave tens of thousands of Jewish settlers on the other side, but has relented under growing public pressure following scores of suicide attacks by Palestinian militants.
Israel faces heavy opposition to the Ariel section from the United States which fears the barrier will create facts on the ground and pre-empt peace talks.
In more than 100 suicide attacks during three years of violence, hundreds of Israelis have been killed. Dozens of times, bombers have simply walked across the unmarked line between Israel and the West Bank, blowing themselves up in Israeli cities.
In the Gaza Strip on Wednesday, troops searching for weapon smuggling tunnels along the Egyptian border blew up one tunnel and destroyed several nearby buildings, the army and Palestinian witnesses said.
Palestinian security sources said that two of the 13 buildings destroyed were inhabited.
The army said that the buildings were used to hide weapons and that troops came under fire from Palestinian gunmen who also set off explosive devices.