Sharon said in a speech Thursday that while he still wants the armed groups dismantled, any crackdown would be "complicated." He said he now considers Palestinian efforts to stop incitement against Israel as a sufficient sign of goodwill.
Palestinians have refused to confront the militants, saying they fear civil war, and the standoff was one of the key obstacles in resuming negotiations.
Israeli commentators described Sharon's shift in position as dramatic.
"There is no longer the demand ... of total war by the Palestinian Authority on terror groups, collecting weapons and governmental reform," said a commentary in the Yediot Ahronot daily Friday.
But Sharon also said Palestinian incitement against Israel must stop, reports CBS News Correspondent Robert Berger, and in two ways.
"One is the cessation of poisonous propaganda and continuing incitement in the Palestinian television and media, second a drastic change in the Palestinian educational system, ending incitement and demonization of Israel, the Israelis and the Jews."
Asked about Sharon's comments, interim Palestinian leader Mahmoud Abbas said the issue of how to handle the militants would have to be raised in future contacts with Israel. "We have our share to do, but they (the Israelis) have more," he said Friday.
Sharon's conciliatory tone comes amid international efforts to restart the peace process in a spirit of hope after Yasser Arafat's death last week. U.S. Secretary of State Colin Powell and foreign ministers from Britain, Russia and other Western nations are expected in the region next week.
Palestinian officials said Powell would arrive for talks in the West Bank town of Jericho on Monday. British Foreign Secretary Jack Straw was expected on Wednesday and Spanish Foreign Minister Miguel Moratinos on Dec. 2.
In the Gaza Strip, Abbas held meetings over several days with rival factions, including the Islamic militant Hamas, the largest opposition group. Abbas is trying to get them to agree to a cease-fire ahead of the Jan. 9 election of a Palestinian Authority president.
Abbas said the meetings went well, although it remained unclear whether he won any assurances from militants. "All this goes toward reorganizing the Palestinian house, to allow every citizen to live in security and hope in a Palestinian state," he said.
Abbas has rejected demands by Hamas and Islamic Jihad to hold legislative and municipal elections on the same day as the presidential elections. The militants are not fielding candidates in the presidential elections but expect to do well in the legislative and municipal vote.
In a gesture to the opposition groups, Abbas' Fatah movement said it would push for municipal and legislative elections by June.
Meanwhile, outrage over an Israeli mistake that left three Egyptian border policemen dead dominated the headlines in Egypt Friday, as the Israeli army chief promised an investigation.
The accidental killing comes at a bad time because Israel wants Egypt to help secure Gaza after the planned Israeli pullout from the area next year, said Israeli analyst Akiva Eldar.
"This will not add any appetite to the Egyptian motivation to get involved in this project," the Haaretz newspaper columnist said.
It was a costly mistake for Israel, and in the Middle East, mistakes are not easily forgiven.
Arafat's death has opened up the political arena, encouraging even independents and political outsiders to run for president. Starting Saturday, candidates can formally put forward their names. Among those planning to announce bids are Sheik Talal Sidr, a former Hamas leader who joined forces with Arafat in 1996, and Abdel Sattar Qassem, a political science professor and anti-corruption crusader.
In Fatah, meanwhile, Abbas' nomination as presidential candidate is not assured.
The old guard of politicians led by Abbas is being challenged by younger activists who demand a share of power after being excluded during the Arafat years. The young guard is led by Marwan Barghouti, an uprising leader jailed by Israel and according to polls far more popular than Abbas. Barghouti is planning to run as an independent unless Fatah holds a primary to choose its candidate, sources close to him have said. However, such a primary is unlikely.
Israeli Foreign Minister Silvan Shalom told Israel Radio on Friday that Israel would keep its distance until a new Palestinian leadership has emerged.
In an apparent reference to Abbas and Qureia, two pragmatists who oppose violence, Shalom said: "I don't think they are really interested in contacts with Israel before the new chairman is elected ... That could harm their chances of being elected or even their chances of staying alive."
Shalom said any Israeli gestures to the Palestinians, including an easing of strict travel bans in the West Bank and Gaza Strip, would also have to wait until after the Palestinian elections.
Sharon, meanwhile, indicated that he is ready to drop a key precondition for peace talks — the dismantling of Palestinian militant groups.
Such a crackdown is listed as one of the Palestinian obligations in the U.S.-backed "road map" peace plan, launched in June 2003, but never implemented. Abbas and Qureia have said they would not confront the militants, but would try to persuade them to disarm. Israel also failed to meet its basic obligations, including a settlement freeze.
Sharon said on Thursday that Israel would insist the militants be disarmed eventually, but added that "it is clear that it's a complicated process."