Speaking at an annual academic conference in Herzliya, north of Tel Aviv, Sharon said that next year could bring a "historic breakthrough" in Israel's relations with the Palestinians.
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Sharon said that Israel must not miss the current opportunity for peace. "We have no desire to rule over you and control your affairs," he said, addressing the Palestinians, endorsing their desire for an independent state while demanding that they stop attacks against Israel.
He said a key element is implementation of his plan to pull Israeli settlements out of the Gaza Strip and a part of the West Bank. "To do this, we have to take the initiative," he said."
Sharon said that Israel's pullout from Gaza would ease demographic pressures on the country. About 8,200 Israeli settlers live among more than 1 million Palestinians in Gaza.
"It is clear that in a permanent peace accord, we will not be in Gaza," he said.
Sharon said that the Palestinians must "eliminate terrorism" as a condition for progress toward a peace settlement with Gaza.
Sharon repeated his pledge to cooperate with the Palestinians to allow free elections on Jan. 9 to replace Yasser Arafat. He said Israel would be prepared to coordinate its pullout from Gaza with a Palestinian leadership that would take responsibility.
The Israeli leader said the Palestinians should have their own state, because to continue Israeli control over Palestinian areas would mean "one people maintaining control of another people," an untenable situation.
Sharon praised Egyptian cooperation and a recent improvement in relations. He said that if Egypt works to prevent Palestinian arms smuggling through tunnels under the border, Israel would withdraw from the "Philadelphia Corridor," the wide border road Israel patrols there.
Palestinians want the London conference to be a high-level gathering that will be a springboard for restarting peace negotiations, based on the internationally backed "road map" peace plan.
"I think the focus should be on substance, and the substance here is ending the Israeli occupation," said Cabinet minister Saeb Erekat.
Israeli Foreign Minister Silvan Shalom said one of the reasons for the conference is to isolate the Palestinian extremists.
"We must all do everything in our power now to strengthen the moderates," he said.
The London conference is "maybe the most significant development in the near future," said Dov Weisglass, a top aide to Sharon.
"It will be a meeting between Palestinians, a few European countries and a few American officials," he said. "It will entirely be focused on how the world can help the Palestinians prepare themselves for the new era."
He also praised the new Palestinian leadership as "normal people" with which Israel can do business.