Asked by the newspaper Haaretz whether Arafat and Nasrallah are targets for assassination, Sharon said: "I wouldn't suggest that either of them feel immune ... Anyone who kills a Jew or harms an Israeli citizen, or sends people to kill Jews, is a marked man. Period."
Sharon told the newspaper Maariv that Arafat "has no insurance policy." Sharon added that "today, everyone knows Arafat is the obstacle (blocking) any progress."
Palestinian officials said they are taking Sharon's threats seriously. "With these threats, Sharon is threatening the future of the peace process in the region," said Arafat aide Nabil Abu Rdeneh.
A spokesman for Nasrallah declined comment.
Israeli police stormed a disputed Jerusalem holy site after Muslim prayers on Friday, firing stun grenades and tear gas, but no injuries were reported.
Officers entered the Al Aqsa Mosque compound after Muslim worshippers threw stones at police deployed nearby, police spokesman Shmuel Ben-Ruby said.
Ben-Ruby said the rock throwers were quickly subdued.
The mosque compound is known to Jews as the Temple Mount, site of biblical Jewish temples. The walled site is revered by Muslims and Jews and is one of the flashpoints in the Israeli-Palestinian conflict.
Sharon's warnings were reinforced by his vice premier and confidant, Ehud Olmert.
"Those involved in killing Jews will have to defend themselves, run away, hide and invest all their energy in defending themselves, that is what the prime minister said," Olmert told Israel Radio.
Israel's army chief, Lt. Gen. Moshe Yaalon, made veiled threats against Arafat and Nasrallah last week, after Israel assassinated Hamas founder Sheik Ahmed Yassin. However, security officials said at the time there were no plans to target the two.
Sharon has repeatedly accused Arafat of involvement in attacks on Israelis, saying he encourages and finances militants. Nasrallah said earlier this week Hezbollah will help Hamas avenge the Yassin killing.
In September, Israel's Cabinet decided that Arafat should be "removed" - an intentionally vague statement that could mean he would be expelled or killed. However, Israel has not acted on the threat.
For more than two years, Israel has confined Arafat to his headquarters in the West Bank city of Ramallah.
Sharon's comments, an escalation in rhetoric, came in newspaper interviews published Friday, in which he also said he favors Israeli withdrawal from all of the Gaza Strip and the West Bank settlements of Ganim, Kadim, Homesh and Sanur, for the first time revealing the scope of his unilateral "disengagement" plan. His spokesman confirmed the remarks.
Sharon furthermore hinted at a timetable, saying he hoped by this time next year Israel would be withdrawing.
Sharon also commented on the bribe-taking suspicions against him, saying: "My hands are clean." Israel's chief prosecutor has recommended he be indicted, but the final decision is up to the attorney general who is expected to rule by the end of May.
The prime minister has said he would let his divided Likud Party make a final decision on the Gaza withdrawal plan. Sharon is to hold a binding referendum among 200,000 party members after his return from an April 14 meeting with U.S. President George W. Bush. Recent polls suggested that while Sharon has an advantage, the gap is too small to assure approval of the Gaza plan.
Sharon's interviews with the Maariv, Yediot Ahronot and Haaretz dailies, given ahead of next week's Passover holiday, are seen as the opening of his campaign for the withdrawal plan.
Maariv quoted him as saying Israel would withdraw from all of Gaza, only retaining control over a patrol road between southern Gaza and the Egyptian border, to prevent weapons smuggling.
"He said very clearly we are not going to stay in Gaza," Sharon's spokesman Raanan Gissin said Friday.
Sharon initially considered retaining three settlements in northern Gaza. There had also been debate over how many West Bank settlements to evacuate, and it appears Sharon settled for the smallest proposed number of four.
"We need to get out of Gaza, not to be responsible any more for what happens there," Sharon told Maariv. "I hope that by next Passover we will be in the midst of disengagement, because disengagement is good for Israel."
The prime minister told Yediot that after the withdrawal Israel would consider cutting off water and electricity to Gaza if attacks against Israelis continue.
Sharon told Haaretz that once Israel completes its West Bank separation barrier, Palestinians living illegally in Israel will be expelled. He said there are tens of thousands of them in Israeli Arab villages.
In other developments Friday, Israeli tanks entered the Rafah refugee camp in Gaza, in a "limited operation" the military said was focused on finding and destroying tunnels used by Palestinians to smuggle in weapons from Egypt.
Rafah is on the Egyptian border.
Witnesses say there were heavy exchanges of fire between Israeli soldiers and Palestinian gunmen. Palestinians say a 19-year-old man was killed. Hospital officials identify him as Mohammed Abed. It is not clear at this point if he was a militant or a civilian.
The Israeli military denies that soldiers fired any shots, but said an armored vehicle was lightly damaged by a roadside bomb.
On Thursday, American diplomats assured skeptical Palestinian officials that Israel's plan to pull out of Gaza brings an opportunity to revive the international "road map" peace initiative, but they said future progress would depend on a Palestinian crackdown on violent groups.