The limits of Israeli Prime Minister Ariel Sharon's strategy to isolate, undermine and eliminate Palestinian Authority President Yasser Arafat were plainly evident last week. Although recent events have given Israel the upper hand in the struggle against Palestinians and Islamic extremists -- the two are not identical -- the prime minister must avoid over-reaching. His goal must be the peace and security of his country; the world will not accept a strategy that foists perpetual insecurity and dependence on the Palestinian people. At times, Mr. Sharon appears to desire just that.

Israel's leader has never had any great fondness for his Palestinian counterpart. In a recent interview with the Israeli newspaper Maariv, Mr. Sharon admitted his regret for not having "eliminated" Mr. Arafat when Israel invaded Lebanon in the 1980s. Today, the prime minister considers Mr. Arafat to be someone with whom he could never again do business. "He's not a partner, he won't be a partner and he is irrelevant," Mr. Sharon explained.

Although the United States shares the Israeli leader's suspicions, President George W. Bush is not yet willing to go that far. Washington has taken a harder line against Mr. Arafat and has acquiesced to Israeli tactics that make Mr. Arafat a virtual prisoner in his own compound. Mr. Bush has demanded that the Palestinian leader take action to stop the violence in the region and blamed him for the attempt to smuggle in weapons last month. Nonetheless, while meeting with Mr. Sharon last week, Mr. Bush made clear the limits of his support for the Israeli prime minister. "The United States will . . . remain engaged with the Palestinian Authority," explained the president's spokesman.