The 22-year-old said Sharon was responsible for the death of two settlers killed in recent months in the West Bank town, the spokesman reported on Monday.
"I have no problem if he is killed," the young man allegedly said during a late Sunday vigil near the central Jerusalem residence. The suspect then ran away, but was later arrested unarmed.
Even the vaguest threats against leaders can spark a major alert in Israel after the assassination by a Jewish extremist of then Prime Minister Yitzhak Rabin in November 1995.
Security around Sharon was reportedly beefed up in the wake of a 4 June summit in Jordan, which saw the launch of the “road map” for peace.
Those concerns focused on Jewish extremists angered at his pledges to dismantle settlement outposts and accept the concept of a future Palestinian state.
All Israeli settlements in the occupied Palestinian territories are illegal under international law. The so-called road map calls for an immediate freeze on all settlement building activity.