There are encouraging signs that Israeli Prime Minister Ariel Sharon may recover from the massive stroke he suffered last week. Such a recovery, his doctor warned, will likely be limited to “basic functions,” leaving a return to politics extremely unlikely. What Israel needs now is a leader who will follow the course laid out by Mr. Sharon.

Elections are scheduled for late March and with Mr. Sharon’s sudden departure from politics, the outcome is now uncertain. Unable to work with the hardliners in his Likud Party, Mr. Sharon in November created a new party, Kadima, which means forward. Polls taken before Mr. Sharon fell ill showed the party would sweep the upcoming parliamentary elections. His deputy, Ehud Olmert, is expected to head up the fledgling centrist party.

The question is whether Mr. Olmert, the former mayor of Jerusalem who has limited foreign policy experience, can continue the tenuous peace that Mr. Sharon managed to forge with the Palestinians. Peace, Israelis in marketplaces and standing vigil outside the hospital where their prime minister was emerging from a coma, is what they want most.

Mr. Sharon, a part of Israel’s founding generation and a major general who had fought in all the country’s wars, found an unexpected path to peace. Arguing that Palestinian leaders were unable to stop the attacks that had left 1,000 Israelis dead since 2001 (3,000 Palestinians were killed), Mr. Sharon opted for security first. He unilaterally ordered the evacuation of Israeli settlements in the Gaza Strip and the return of the land to the Palestinians.

The handover this summer went surprisingly well. Perhaps more controversial is the building of a barrier, sometimes fence, sometimes concrete wall, to separate Israel from the Palestinian territories. Still, attacks have declined dramatically and Mr. Sharon’s popularity soared.

Mr. Sharon’s turn from fighter to pragmatist was based largely on demographics. He understood that Palestinians, with much higher birthrates than their neighbors, would soon outnumber Israelis. As a result, he knew that territory must be divided, and protected. Going back to a policy of expanded settlements, which some like former Prime Minister Benjamin Netanyahu favor, would be a step backward.

The challenge for Mr. Olmert, or whoever emerges to lead Israel, is to continue the work that Mr. Sharon left unfinished.