The daily Haaretz reported that a Labor Cabinet minister and representative from the Likud and Center parties are working to build a movement advocating "separation" from the Palestinians.
The idea of simply cutting Israel off from the Palestinian territories has been talked about for years.
It would mean building a border-style fence along the line between Israel and the West Bank, possibly keeping settlements close to the line inside Israeli-controlled territory. The purpose would be to keep violent Palestinian militants out of Israel and reduce friction between Israelis and Palestinians.
Critics charge that it would mean handing over large parts of the West Bank to the Palestinians without a peace accord and would not end the conflict.
Sharon has instructed his police and military to beef up security along the Israel-West Bank line, but he opposes marking a border unilaterally.
A poll published Friday in the Maariv daily showed that about half the Israelis favor tougher military measures against the Palestinians, a sharp increase from a poll just a week earlier.
The Gallup poll showed that 51 percent of the Israelis surveyed believe that their army is not using enough force against the Palestinians. Only 17 percent felt too much force was being used, and 24 percent said the present level is correct.
Learn more about the history of the Arab-Israeli conflict.
The poll questioned 593 Israeli adults and quoted a 4.5 percent margin of error.
Last week's poll showed 42 percent in favor of additional measures. In the meantime, there were two suicide bombing attacks by Palestinian militants, including one in downtown Jerusalem that killed 15 people and the bomber.
Since the fighting began last September, 569 people have been killed on the Palestinian side, and 152 people have been killed on the Israeli side.
Another significant change emerged from a question asking whether Sharon would succeed in stopping Palestinian terror and violence. In the poll published Friday, only 21 percent felt he would, while fully 70 percent felt he would fail. In the last poll, 43 percent believed Sharon could end the violence, and 41 percent disagreed.
Sharon accuses Palestinian leader Yasser Arafat of giving free rein to militants and has refused to resume peace negotiations until there is a complete halt to violence.
The Palestinians say talks cannot take place until Israel withdraws from nine Palestinian offices it sezed in and around Jerusalem last Friday, including Orient House, the unofficial PLO headquarters in the city.
At the United Nations, the Palestinians launched another quest for foreign action after Israel responded to the recent suicide attacks by seizing Palestinian offices in and around Jerusalem and briefly sending tanks into the West Bank town of Jenin.
The 15-member Security Council scheduled an open meeting for Monday for U.N. members to express their views as requested by the 57-member Organization of the Islamic Conference. Palestinians hope the debate will lead to a formal resolution.
Two protracted attempts to get the council to authorize or even suggest an observer force in a resolution failed over the last year with the United States casting a veto in March.
In Gaza, Palestinian witnesses said Israeli had troops shot and slightly wounded two youngsters, aged nine and 16, at the Brazil refugee camp near Rafah on the border with Egypt.
Israel said it was on high alert for suicide bombings by the Muslim militant groups Hamas and Islamic Jihad.
In Gaza, a man who died while being interrogated by Palestinian police was taken for burial by his family Friday. He was suspected of collaborating with Israel and was apparently tortured. According to human rights activist Bassam Eid, 25 people have died in Palestinian detention since the Palestinian Authority was set up in 1994.
Meanwhile, Egypt put ideas about Middle East peace to the United States and said it might be able to announce more details in two days.
Osama al-Baz, political adviser to Egyptian President Hosni Mubarak, said after talks with Secretary of State Colin Powell that he also had assurances the United States would be active in Middle East peacemaking.
Powell agreed, saying: "We both committed ourselves to doing everything we can to get us close to that day when the Mitchell plan can begin its implementation and execution."
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