Last month, Israel's Cabinet decided to "remove" the Palestinian at an unspecified time, prompting speculation it would either expel or assassinate him.
"I don't see any plans to kill him," Sharon said Monday, while accusing Arafat of orchestrating attacks on Israelis during three years of fighting.
"You don't have to worry, he's alive and not only is he alive but very active in taking all the ... steps ... that bring to murder of children, civilians, the old," Sharon told a group of European legislators.
Egypt has resumed its efforts to persuade militant Palestinian groups to halt their attacks on Israelis, Egyptian and Palestinian officials said Monday.
The resumption of the Egyptian mediation came in response to a request by Palestinian Authority Prime Minister Ahmed Qureia, who visited Cairo last week, the officials said.
"The situation is getting out of control and it is about time that something is done to stop it," an Egyptian official told The Associated Press on condition of anonymity. He said Egypt will try to arrange for a new cease-fire, similar to the one it persuaded radical groups to declare earlier this year.
Egypt, which in 1979 became the first Arab nation to sign a peace treaty with Israel, is seen as a key Arab moderate and peace mediator.
However, Hamas Sunday denied reports it was interested in a new cease-fire agreement. It had been reported that Qureia had asked to meet with Hamas leaders.
Qureia, meanwhile, said he welcomed the prospect of talks with Hamas on halting attacks on Israelis. The Islamic militant group, which just several days earlier had taken part in a deadly attack on a Jewish settlement in Gaza, said Sunday it was ready to hear Qureia's truce proposals.
Qureia's term as head of an emergency Cabinet expires Nov. 4, just a month after he took office, and he has said he does not want to continue as prime minister. However, there is growing expectation that Yasser Arafat will reappoint Qureia, despite their disagreements over control of the security services.
Qureia has said he wants to negotiate a truce with Israel, and for that he'd need assurances from Hamas, Islamic Jihad and other militants that they are ready to halt attacks on Israelis.
Also Monday, Israel's Defense Ministry confirmed it will provide services to eight West Bank settlement outposts, despite the government's earlier pledge to remove them as part of a stalled U.S.-backed peace plan.
Dismantling dozens of unauthorized settlement outposts was one of Israel's obligations under the "road map" peace plan, which was launched in June with great fanfare, but quickly bogged down over disagreements and violence.
Palestinians complained that Israel is systematically undermining the road map.
Israeli officials counter that the Palestinians have ignored their commitment to dismantle terrorist groups, so Israel will not make unilateral concessions on the settlements, reports CBS News Correspondent Robert Berger.
Also Monday, one Palestinian was killed, one wounded and three were detained by Israeli troops near the border fence between the Gaza Strip and Israel. It was not clear whether the five were trying to sneak into Israel, the army said.
The outposts will be fenced in and receive lighting, and children living there will be bused to schools, said a ministry official, who spoke on condition of anonymity.
The assurances were given to residents of the outpost in a letter by Ron Shechner, the settlement adviser of Defense Minister Shaul Mofaz.
Shechner told the Yediot Ahronot daily that this does not mean the outposts are being legalized. However, the decision appears to imply recognition, and as such would violate Israel's promise to the United States not to establish new settlements.
The Israeli group Peace Now, which monitors settlement expansion, said that when the road map was launched, there were 104 outposts. Since then, the military has dismantled seven, but five more were established, bringing the latest total to 102. Peace Now spokesman Dror Etkes said the population in the outposts has grown.
"These actions have to be condemned by the United States and the Quartet (of Mideast mediators) and I call upon them to intervene immediately," Palestinian negotiator Saeb Erekat said.