JERUSALEM — A surge in violence this week cost some two dozen Israelis their lives — and put Prime Minister Ariel Sharon’s political life increasingly at peril.

A year after Sharon took office with a pledge to restore security, Israelis were besieged with terror coming from every direction and with almost every weapon — suicide bombings, sniper shots, Kassam missiles and stabbings.

Sharon’s response? Hit the Palestinians again, and harder.

On Monday, Sharon said the Palestinians must be dealt a blow so severe that they will finally understand that terror damages their cause.

Only then, he said, may the Palestinians be convinced to abandon violence and return to the negotiating table.

Sharon’s remarks were met with criticism on Wednesday by Secretary of State Colin Powell, who said, “If you declare war against the Palestinians and think you can solve the problem by seeing how many Palestinians can be killed, I don’t know if that leads you anywhere.”

In a meeting with a house subcommittee, Powell also had harsh words for Palestinian leader Yasser Arafat, suggesting that he could pick up the phone and order a stop to the terrorist attacks.

Israelis increasingly are dubious that Sharon can lead them out of the present impasse.

Public opinion polls show Sharon’s approval ratings plummeting from the highs he enjoyed for most of his first year in office. In addition, a Saudi Arabian peace initiative threatens to expose the gap between Sharon’s goals and the Bush administration’s vision of Mideast peace, setting up a potential confrontation between Jerusalem and Washington.

Never formally presented but gathering steam nonetheless, the Saudi plan calls for the Arab world to make peace with Israel in exchange for a complete Israeli withdrawal from all land captured in the 1967 Six-Day War.

Washington has welcomed the initiative and is exploring it, while Sharon said this week that a return to those borders — which leaves Israel just nine miles wide at its most populated point — endangers the country’s security.

A poll published last Friday in the Maariv daily newspaper found that 53 percent of those surveyed were unhappy with Sharon’s first year in office. The poll also found 61 percent dissatisfied with Sharon’s efforts to improve Israel security, and only 28 percent felt it was matched their expectations.

In addition an opinion poll by the influential Tami Steinmetz Center at Tel Aviv University showed a steep drop — from more than 40 percent to just 26 percent — in the number of Israelis who agree with Sharon that “Israel can change the situation by the use of more military force.”

At the same time, however, only 27 percent believe that diplomacy can resolve the conflict, as Labor Party Foreign Minister Shimon Peres proposes.

If those messages seem contradictory, it’s no accident.

After nearly 18 months, the increasingly bloody Palestinian intifada shows no signs of abating, and more people on both sides are describing the deteriorating conflict as outright war.

The second-ranking Likud Party minister demanded Tuesday that Israel oust Arafat from the Palestinian territories.

Finance Minister Silvan Shalom admitted that his position was not shared by Sharon — not yet, or at least not publicly — but he warned that “the moment of decision is approaching.”

Sharon reiterated his determination to strike hard at the Palestinians, but he had to shelve a proposal to send Israeli tanks back to besiege Arafat’s office in Ramallah in the face of strong opposition from the defense minister and Labor Party leader, Benjamin Ben-Eliezer.

Political commentators predict that the longevity of the unity government is in doubt as the violence spirals. Israelis this week had to contemplate the daunting prospect of political instability — and, possibly, early elections.

The inter-ministerial disputes also exacerbate a widely held concern that the politicians, both in the unity government and in the opposition, have no workable policy to offer.

Sharon himself, in a series of briefings and comments Monday, told the Knesset and reporters that there is “no diplomatic outlook at this time, only a military outlook.”

The explicit denial of any diplomatic strategy could help Sharon fend off the remorseless pressure he faces from the right — led by ex-Prime Minister Benjamin Netanyahu — that wants him to topple the Palestinian Authority and root out the terrorist infrastructure it has cultivated in the West Bank and Gaza Strip.

Increasingly, the barrenness of Sharon’s diplomatic field ups the pressure on the Labor Party to secede from the unity government.

Ben-Eliezer is said to predict privately that Labor will leave within weeks or months when a suitable situation presents itself.

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